메뉴 건너뛰기




Volumn , Issue , 2006, Pages 1-664

Numerical optimization

Author keywords

[No Author keywords available]

Indexed keywords


EID: 85098056778     PISSN: 14318598     EISSN: 21971773     Source Type: Book Series    
DOI: None     Document Type: Chapter
Times cited : (1285)

References (322)
  • 2
    • 0002662980 scopus 로고
    • On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method
    • ), pp
    • H. AKAIKE, On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method, Annals of the Institute of Statistical Mathematics, 11 (1959), pp. 1–17.
    • (1959) Annals of the Institute of Statistical Mathematics , vol.11 , pp. 1-17
    • Akaike, H.1
  • 3
    • 77957214026 scopus 로고
    • Descent property and global convergence of the Fletcher-Reeves method with inexact line search
    • ), pp
    • M. AL-BAALI, Descent property and global convergence of the Fletcher-Reeves method with inexact line search, I.M.A. Journal on Numerical Analysis, 5 (1985), pp. 121–124.
    • (1985) I.M.A. Journal on Numerical Analysis , vol.5 , pp. 121-124
    • Al-Baali, M.1
  • 6
    • 0000728112 scopus 로고    scopus 로고
    • Implementation of interior-point methods for large scale linear programming, in Interior Point Methods in Mathematical Programming, T. Terlaky, ed
    • pp
    • E. D. ANDERSEN, J. GONDZIO, C. MÉSZÁROS, AND X. XU, Implementation of interior-point methods for large scale linear programming, in Interior Point Methods in Mathematical Programming, T. Terlaky, ed., Kluwer, 1996, ch. 6, pp. 189–252.
    • Kluwer, 1996, Ch , vol.6 , pp. 189-252
    • Andersen, E.D.1    Gondzio, J.2    Mészáros, C.3    And, X.X.4
  • 8
    • 27844590714 scopus 로고    scopus 로고
    • On solving mathematical programs with complementarity constraints as nonlinear programs
    • ), pp
    • M. ANITESCU, On solving mathematical programs with complementarity constraints as nonlinear programs, SIAM Journal on Optimization, 15 (2005), pp. 1203–1236.
    • (2005) SIAM Journal on Optimization , vol.15 , pp. 1203-1236
    • Anitescu, M.1
  • 9
    • 85098052715 scopus 로고    scopus 로고
    • ARKI CONSULTING AND DEVELOPMENT A/S, CONOPT version 3, 2004
    • ARKI CONSULTING AND DEVELOPMENT A/S, CONOPT version 3, 2004.
  • 11
    • 1842721334 scopus 로고    scopus 로고
    • P. BAPTIST AND J. STOER, On the relation between quadratic termination and convergence properties of minimization algorithms, Part II: Applications, Numerische Mathematik, 28 (1977), pp. 367– 392
    • P. BAPTIST AND J. STOER, On the relation between quadratic termination and convergence properties of minimization algorithms, Part II: Applications, Numerische Mathematik, 28 (1977), pp. 367– 392.
  • 12
    • 0001637146 scopus 로고
    • The simplex method of linear programming using LU decomposition
    • ), pp
    • R. H. BARTELS AND G. H. GOLUB, The simplex method of linear programming using LU decomposition, Communications of the ACM, 12 (1969), pp. 266–268.
    • (1969) Communications of the ACM , vol.12 , pp. 266-268
    • Bartels, R.H.1    Golub, G.H.2
  • 13
    • 85098060067 scopus 로고    scopus 로고
    • R. BARTLETT AND L. BIEGLER, rSQP++: An object-oriented framework for successive quadratic programming, in Large-Scale PDE-Constrained Optimization, L. T. Biegler, O. Ghat-tas, M. Heinkenschloss, and B. van Bloemen Waanders, eds., vol. 30, New York, 2003, Springer-Verlag, pp. 316–330. Lecture Notes in Computational Science and Engineering
    • R. BARTLETT AND L. BIEGLER, rSQP++: An object-oriented framework for successive quadratic programming, in Large-Scale PDE-Constrained Optimization, L. T. Biegler, O. Ghat-tas, M. Heinkenschloss, and B. van Bloemen Waanders, eds., vol. 30, New York, 2003, Springer-Verlag, pp. 316–330. Lecture Notes in Computational Science and Engineering.
  • 15
    • 85098093288 scopus 로고    scopus 로고
    • A. BEN-TAL AND A. NEMIROVSKI, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, MPS-SIAM Series on Optimization, SIAM, 2001
    • A. BEN-TAL AND A. NEMIROVSKI, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, MPS-SIAM Series on Optimization, SIAM, 2001.
  • 19
    • 84980531554 scopus 로고    scopus 로고
    • Belmont, MA, second ed
    • Nonlinear Programming, Athena Scientific, Belmont, MA, second ed., 1999.
    • (1999) Athena Scientific
  • 20
    • 85098080199 scopus 로고    scopus 로고
    • eds., Computational Differentiation: Techniques, Applications, and Tools, SIAM Publications, Philadelphia, PA
    • M. BERZ, C. BISCHOF, C. F. CORLISS, AND A. GRIEWANK, eds., Computational Differentiation: Techniques, Applications, and Tools, SIAM Publications, Philadelphia, PA, 1996.
    • (1996) GRIEWANK
    • Berz, M.1    Bischof, C.2    Corliss, C.F.3    And, A.4
  • 24
    • 0006910070 scopus 로고    scopus 로고
    • Computing gradients in large-scale optimization using automatic differentiation
    • ), pp
    • C. BISCHOF, A. BOUARICHA, P. KHADEMI, AND J. J. MORÉ, Computing gradients in large-scale optimization using automatic differentiation, INFORMS Journal on Computing, 9 (1997), pp. 185–194.
    • (1997) INFORMS Journal on Computing , vol.9 , pp. 185-194
    • Bischof, C.1    Bouaricha, A.2    Khademi, P.3    Moré, J.J.4
  • 26
    • 0027903541 scopus 로고
    • Structured second-and higher-order derivatives through univariate Taylor series
    • ), pp
    • C. BISCHOF, G. CORLISS, AND A. GRIEWANK, Structured second-and higher-order derivatives through univariate Taylor series, Optimization Methods and Software, 2 (1993), pp. 211–232.
    • (1993) Optimization Methods and Software , vol.2 , pp. 211-232
    • Bischof, C.1    Corliss, G.2    Griewank, A.3
  • 27
    • 0030300311 scopus 로고    scopus 로고
    • Efficient computation of gradients and Jaco-bians by transparent exploitation of sparsity in automatic differentiation
    • ), pp
    • C. BISCHOF, P. KHADEMI, A. BOUARICHA, AND A. CARLE, Efficient computation of gradients and Jaco-bians by transparent exploitation of sparsity in automatic differentiation, Optimization Methods and Software, 7 (1996), pp. 1–39.
    • (1996) Optimization Methods and Software , vol.7 , pp. 1-39
    • Bischof, C.1    Khademi, P.2    Bouaricha, A.3    Carle, A.4
  • 28
    • 0031383181 scopus 로고    scopus 로고
    • ADIC: An extensible automatic differentiation tool for ANSI-C
    • ), pp
    • C. BISCHOF, L. ROH, AND A. MAUER, ADIC: An extensible automatic differentiation tool for ANSI-C, Software—Practice and Experience, 27 (1997), pp. 1427–1456.
    • (1997) Software—Practice and Experience , vol.27 , pp. 1427-1456
    • Bischof, C.1    Roh, L.2    Mauer, A.3
  • 32
    • 0009575103 scopus 로고
    • Convergence properties of a class of rank-two updates
    • ), pp
    • P. T. BOGGS AND J. W. TOLLE, Convergence properties of a class of rank-two updates, SIAM Journal on Optimization, 4 (1994), pp. 262–287.
    • (1994) SIAM Journal on Optimization , vol.4 , pp. 262-287
    • Boggs, P.T.1    Tolle, J.W.2
  • 33
    • 44649149897 scopus 로고    scopus 로고
    • pp
    • Sequential quadratic programming, Acta Numerica, 4 (1996), pp. 1–51.
    • (1996) Acta Numerica , vol.4 , pp. 1-51
  • 34
    • 0020099933 scopus 로고
    • On the local convergence of quasi-Newton methods for constrained optimization
    • ), pp
    • P. T. BOGGS, J. W. TOLLE, AND P. WANG, On the local convergence of quasi-Newton methods for constrained optimization, SIAM Journal on Control and Optimization, 20 (1982), pp. 161–171.
    • (1982) SIAM Journal on Control and Optimization , vol.20 , pp. 161-171
    • Boggs, P.T.1    Tolle, J.W.2    Wang, P.3
  • 36
    • 0026908925 scopus 로고
    • Avoiding the Maratos effect by means of a nonmonotone line search. II. Inequality constrained problems — feasible iterates
    • ), pp
    • J. F. BONNANS, E. R. PANIER, A. L. TITS, AND J. L. ZHOU, Avoiding the Maratos effect by means of a nonmonotone line search. II. Inequality constrained problems — feasible iterates, SIAM Journal on Numerical Analysis, 29 (1992), pp. 1187–1202.
    • (1992) SIAM Journal on Numerical Analysis , vol.29 , pp. 1187-1202
    • Bonnans, J.F.1    Panier, E.R.2    Tits, A.L.3    Zhou, J.L.4
  • 42
    • 84966228742 scopus 로고
    • Some stable methods for calculating inertia and solving symmetric linear systems
    • ), pp
    • J. R. BUNCH AND L. KAUFMAN, Some stable methods for calculating inertia and solving symmetric linear systems, Mathematics of Computation, 31 (1977), pp. 163–179.
    • (1977) Mathematics of Computation , vol.31 , pp. 163-179
    • Bunch, J.R.1    Kaufman, L.2
  • 43
    • 0015200767 scopus 로고
    • Direct methods for solving symmetric indefinite systems of linear equations
    • ), pp
    • J. R. BUNCH AND B. N. PARLETT, Direct methods for solving symmetric indefinite systems of linear equations, SIAM Journal on Numerical Analysis, 8 (1971), pp. 639–655.
    • (1971) SIAM Journal on Numerical Analysis , vol.8 , pp. 639-655
    • Bunch, J.R.1    Parlett, B.N.2
  • 46
    • 85098079621 scopus 로고    scopus 로고
    • Knitro: An integrated package for nonlinear optimization
    • Optimization Technology Center, Evanston, IL, June
    • R. BYRD, J. NOCEDAL, AND R. WALTZ, Knitro: An integrated package for nonlinear optimization, Technical Report 18, Optimization Technology Center, Evanston, IL, June 2005.
    • (2005) Technical Report , vol.18
    • Byrd, R.1    Nocedal, J.2    Waltz, R.3
  • 47
    • 85098059169 scopus 로고    scopus 로고
    • R. BYRD, J. NOCEDAL, AND R. A. WALTZ, Steering exact penalty methods, Technical Report OTC 2004/07, Optimization Technology Center, Northwestern University, Evanston, IL, USA, April 2004
    • R. BYRD, J. NOCEDAL, AND R. A. WALTZ, Steering exact penalty methods, Technical Report OTC 2004/07, Optimization Technology Center, Northwestern University, Evanston, IL, USA, April 2004.
  • 48
    • 0001130234 scopus 로고    scopus 로고
    • A trust region method based on interior point techniques for nonlinear programming
    • ), pp
    • R. H. BYRD, J.-C. GILBERT, AND J. NOCEDAL, A trust region method based on interior point techniques for nonlinear programming, Mathematical Programming, 89 (2000), pp. 149–185.
    • (2000) Mathematical Programming , vol.89 , pp. 149-185
    • Byrd, R.H.1    Gilbert, J.-C.2    Nocedal, J.3
  • 49
    • 19844377201 scopus 로고    scopus 로고
    • An algorithm for nonlinear optimization using linear programming and equality constrained subproblems
    • ), pp
    • R. H. BYRD, N. I. M. GOULD, J. NOCEDAL, AND R. A. WALTZ, An algorithm for nonlinear optimization using linear programming and equality constrained subproblems, Mathematical Programming, Series B, 100 (2004), pp. 27–48.
    • (2004) Mathematical Programming, Series B , vol.100 , pp. 27-48
    • Byrd, R.H.1    Gould, N.I.M.2    Nocedal, J.3    Waltz, R.A.4
  • 50
    • 0033471382 scopus 로고    scopus 로고
    • An interior point method for large scale nonlinear programming
    • ), pp
    • R. H. BYRD, M. E. HRIBAR, AND J. NOCEDAL, An interior point method for large scale nonlinear programming, SIAM Journal on Optimization, 9 (1999), pp. 877–900.
    • (1999) SIAM Journal on Optimization , vol.9 , pp. 877-900
    • Byrd, R.H.1    Hribar, M.E.2    Nocedal, J.3
  • 51
  • 52
    • 0028319529 scopus 로고
    • Representations of quasi-Newton matrices and their use in limited-memory methods
    • ), pp
    • R. H. BYRD, J. NOCEDAL, AND R. B. SCHNABEL, Representations of quasi-Newton matrices and their use in limited-memory methods, Mathematical Programming, Series A, 63 (1994), pp. 129–156.
    • (1994) Mathematical Programming, Series A , vol.63 , pp. 129-156
    • Byrd, R.H.1    Nocedal, J.2    Schnabel, R.B.3
  • 53
    • 0023427318 scopus 로고
    • Global convergence of a class of quasi-Newton methods on convex problems
    • ), pp
    • R. H. BYRD, J. NOCEDAL, AND Y. YUAN, Global convergence of a class of quasi-Newton methods on convex problems, SIAM Journal on Numerical Analysis, 24 (1987), pp. 1171–1190.
    • (1987) SIAM Journal on Numerical Analysis , vol.24 , pp. 1171-1190
    • Byrd, R.H.1    Nocedal, J.2    Yuan, Y.3
  • 54
    • 34250095268 scopus 로고
    • Approximate solution of the trust regions problem by minimization over two-dimensional subspaces
    • ), pp
    • R. H. BYRD, R. B. SCHNABEL, AND G. A. SCHULTZ, Approximate solution of the trust regions problem by minimization over two-dimensional subspaces, Mathematical Programming, 40 (1988), pp. 247–263.
    • (1988) Mathematical Programming , vol.40 , pp. 247-263
    • Byrd, R.H.1    Schnabel, R.B.2    Schultz, G.A.3
  • 55
    • 0023430609 scopus 로고
    • A trust region algorithm for nonlinearly constrained optimization
    • ), pp
    • R. H. BYRD, R. B. SCHNABEL, AND G. A. SHULTZ, A trust region algorithm for nonlinearly constrained optimization, SIAM Journal on Numerical Analysis, 24 (1987), pp. 1152–1170.
    • (1987) SIAM Journal on Numerical Analysis , vol.24 , pp. 1152-1170
    • Byrd, R.H.1    Schnabel, R.B.2    Shultz, G.A.3
  • 57
    • 0002674910 scopus 로고
    • The watchdog technique for forcing convergence in algorithms for constrained optimization
    • ), pp
    • R. CHAMBERLAIN, C. LEMARECHAL, H. C. PEDERSEN, AND M. J. D. POWELL, The watchdog technique for forcing convergence in algorithms for constrained optimization, Mathematical Programming, 16 (1982), pp. 1–17.
    • (1982) Mathematical Programming , vol.16 , pp. 1-17
    • Chamberlain, R.1    Lemarechal, C.2    Pedersen, H.C.3    Powell, M.J.D.4
  • 58
    • 0039991939 scopus 로고    scopus 로고
    • A modified Cholesky algorithm based on a symmetric indefinite factorization
    • ), pp
    • S. H. CHENG AND N. J. HIGHAM, A modified Cholesky algorithm based on a symmetric indefinite factorization, SIAM Journal of Matrix Analysis and Applications, 19 (1998), pp. 1097–1100.
    • (1998) SIAM Journal of Matrix Analysis and Applications , vol.19 , pp. 1097-1100
    • Cheng, S.H.1    Higham, N.J.2
  • 59
    • 14944352190 scopus 로고    scopus 로고
    • On the global convergence of an SLP-filter algorithm that takes EQP steps
    • ), pp
    • C. M. CHIN AND R. FLETCHER, On the global convergence of an SLP-filter algorithm that takes EQP steps, Mathematical Programming, Series A, 96 (2003), pp. 161–177.
    • (2003) Mathematical Programming, Series A , vol.96 , pp. 161-177
    • Chin, C.M.1    Fletcher, R.2
  • 60
    • 0034345430 scopus 로고    scopus 로고
    • Superlinear convergence and implicit filtering
    • ), pp
    • T. D. CHOI AND C. T. KELLEY, Superlinear convergence and implicit filtering, SIAM Journal on Optimization, 10 (2000), pp. 1149–1162.
    • (2000) SIAM Journal on Optimization , vol.10 , pp. 1149-1162
    • Choi, T.D.1    Kelley, C.T.2
  • 62
    • 0003859933 scopus 로고
    • John Wiley & Sons, New York, (Reprinted by SIAM Publications, 1990)
    • F. H. CLARKE, Optimization and Nonsmooth Analysis, John Wiley & Sons, New York, 1983 (Reprinted by SIAM Publications, 1990).
    • (1983) Optimization and Nonsmooth Analysis
    • Clarke, F.H.1
  • 63
    • 0141937371 scopus 로고
    • Rate of convergence of several conjugate gradient algorithms
    • ), pp
    • A. COHEN, Rate of convergence of several conjugate gradient algorithms, SIAM Journal on Numerical Analysis, 9 (1972), pp. 248–259.
    • (1972) SIAM Journal on Numerical Analysis , vol.9 , pp. 248-259
    • Cohen, A.1
  • 64
    • 85098082477 scopus 로고    scopus 로고
    • T. F. COLEMAN, Linearly constrained optimization and projected preconditioned conjugate gradients, in Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, J. Lewis, ed., Philadelphia, USA, 1994, SIAM, pp. 118–122
    • T. F. COLEMAN, Linearly constrained optimization and projected preconditioned conjugate gradients, in Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, J. Lewis, ed., Philadelphia, USA, 1994, SIAM, pp. 118–122.
  • 65
    • 34250234854 scopus 로고
    • Non-linear programming via an exact penalty-function: Asymptotic analysis
    • ), pp
    • T. F. COLEMAN AND A. R. CONN, Non-linear programming via an exact penalty-function: Asymptotic analysis, Mathematical Programming, 24 (1982), pp. 123–136.
    • (1982) Mathematical Programming , vol.24 , pp. 123-136
    • Coleman, T.F.1    Conn, A.R.2
  • 67
    • 0022229224 scopus 로고
    • Software for estimating sparse Hessian matrices
    • ), pp
    • , Software for estimating sparse Hessian matrices, ACM Transactions on Mathematical Software, 11 (1985), pp. 363–377.
    • (1985) ACM Transactions on Mathematical Software , vol.11 , pp. 363-377
  • 68
    • 0000421410 scopus 로고
    • Estimation of sparse Jacobian matrices and graph coloring problems
    • ), pp
    • T. F. COLEMAN AND J. J. MORÉ, Estimation of sparse Jacobian matrices and graph coloring problems, SIAM Journal on Numerical Analysis, 20 (1983), pp. 187–209.
    • (1983) SIAM Journal on Numerical Analysis , vol.20 , pp. 187-209
    • Coleman, T.F.1    Moré, J.J.2
  • 69
    • 0021408208 scopus 로고
    • Estimation of sparse Hessian matrices and graph coloring problems
    • ), pp
    • , Estimation of sparse Hessian matrices and graph coloring problems, Mathematical Programming, 28 (1984), pp. 243–270.
    • (1984) Mathematical Programming , vol.28 , pp. 243-270
  • 70
    • 84966215545 scopus 로고
    • Testing a class of algorithms for solving minimization problems with simple bounds on the variables
    • ), pp
    • A. R. CONN, N. I. M. GOULD, AND P. L. TOINT, Testing a class of algorithms for solving minimization problems with simple bounds on the variables, Mathematics of Computation, 50 (1988), pp. 399– 430.
    • (1988) Mathematics of Computation , vol.50 , pp. 399-430
    • Conn, A.R.1    Gould, N.I.M.2    Toint, P.L.3
  • 71
    • 33845521414 scopus 로고
    • Convergence of quasi-Newton matrices generated by the symmetric rank one update
    • ), pp
    • Convergence of quasi-Newton matrices generated by the symmetric rank one update, Mathematical Programming, 50 (1991), pp. 177–195.
    • (1991) Mathematical Programming , vol.50 , pp. 177-195
  • 76
    • 0242609515 scopus 로고    scopus 로고
    • Recent progress in unconstrained nonlinear optimization without derivatives
    • ), pp
    • , Recent progress in unconstrained nonlinear optimization without derivatives, Mathematical Programming, Series B, 79 (1997), pp. 397–414.
    • (1997) Mathematical Programming, Series B , vol.79 , pp. 397-414
  • 78
    • 0002249579 scopus 로고    scopus 로고
    • An introduction to automatic differentiation
    • M. Berz, C. Bischof, G. F. Corliss, and A. Griewank, eds., SIAM Publications, Philadelphia, PA, ch. 1
    • B. F. CORLISS AND L. B. RALL, An introduction to automatic differentiation, in Computational Differentiation: Techniques, Applications, and Tools, M. Berz, C. Bischof, G. F. Corliss, and A. Griewank, eds., SIAM Publications, Philadelphia, PA, 1996, ch. 1.
    • (1996) Computational Differentiation: Techniques, Applications, and Tools
    • Corliss, B.F.1    Rall, L.B.2
  • 81
    • 84960798507 scopus 로고
    • Variational methods for the solution of problems with equilibrium and vibration
    • ), pp
    • R. COURANT, Variational methods for the solution of problems with equilibrium and vibration, Bulletin of the American Mathematical Society, 49 (1943), pp. 1–23.
    • (1943) Bulletin of the American Mathematical Society , vol.49 , pp. 1-23
    • Courant, R.1
  • 82
  • 85
    • 0033266804 scopus 로고    scopus 로고
    • A nonlinear conjugate gradient method with a strong global convergence property
    • ), pp
    • Y. DAI AND Y. YUAN, A nonlinear conjugate gradient method with a strong global convergence property, SIAM Journal on Optimization, 10 (1999), pp. 177–182.
    • (1999) SIAM Journal on Optimization , vol.10 , pp. 177-182
    • Dai, Y.1    Yuan, Y.2
  • 88
    • 84964389892 scopus 로고
    • Variable metric method for minimization
    • ), pp
    • , Variable metric method for minimization, SIAM Journal on Optimization, 1 (1991), pp. 1–17.
    • (1991) SIAM Journal on Optimization , vol.1 , pp. 1-17
  • 90
    • 84976747891 scopus 로고
    • Algorithm 573 — NL2SOL, An adaptive nonlinear least-squares algorithm
    • ), pp
    • J. E. DENNIS, D. M. GAY, AND R. E. WELSCH, Algorithm 573 — NL2SOL, An adaptive nonlinear least-squares algorithm, ACM Transactions on Mathematical Software, 7 (1981), pp. 348–368.
    • (1981) ACM Transactions on Mathematical Software , vol.7 , pp. 348-368
    • Dennis, J.E.1    Gay, D.M.2    Welsch, R.E.3
  • 91
    • 0002663672 scopus 로고
    • Quasi-Newton methods, motivation and theory
    • ), pp
    • J. E. DENNIS AND J. J. MORÉ, Quasi-Newton methods, motivation and theory, SIAM Review, 19 (1977), pp. 46–89.
    • (1977) SIAM Review , vol.19 , pp. 46-89
    • Dennis, J.E.1    Moré, J.J.2
  • 92
    • 85098086072 scopus 로고    scopus 로고
    • J. E. DENNIS AND R. B. SCHNABEL, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, NJ, 1983. Reprinted by SIAM Publications, 1993
    • J. E. DENNIS AND R. B. SCHNABEL, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, NJ, 1983. Reprinted by SIAM Publications, 1993.
  • 93
    • 84973057463 scopus 로고
    • J. E. DENNIS AND R. B. SCHNABEL, A view of unconstrained optimization, in Optimization, vol. 1 of Handbooks in Operations Research and Management, Elsevier, Amsterdam, The Netherlands, pp
    • J. E. DENNIS AND R. B. SCHNABEL, A view of unconstrained optimization, in Optimization, vol. 1 of Handbooks in Operations Research and Management, Elsevier Science Publishers, Amsterdam, The Netherlands, 1989, pp. 1–72.
    • (1989) Science Publishers , pp. 1-72
  • 94
    • 0000754239 scopus 로고
    • Iterative solution of problems of linear and quadratic programming
    • ), pp
    • I. I. DIKIN, Iterative solution of problems of linear and quadratic programming, Soviet Mathematics-Doklady, 8 (1967), pp. 674–675.
    • (1967) Soviet Mathematics-Doklady , vol.8 , pp. 674-675
    • Dikin, I.I.1
  • 95
    • 0020822138 scopus 로고
    • The multifrontal solution of indefinite sparse symmetric linear equations
    • ), pp
    • I. S. DUFF AND J. K. REID, The multifrontal solution of indefinite sparse symmetric linear equations, ACM Transactions on Mathematical Software, 9 (1983), pp. 302–325.
    • (1983) ACM Transactions on Mathematical Software , vol.9 , pp. 302-325
    • Duff, I.S.1    Reid, J.K.2
  • 96
    • 0030164754 scopus 로고    scopus 로고
    • The design of MA48: A code for the direct solution of sparse unsymmetric linear systems of equations
    • ), pp
    • I. S. DUFF AND J. K. REID, The design of MA48: A code for the direct solution of sparse unsymmetric linear systems of equations, ACM Transactions on Mathematical Software, 22 (1996), pp. 187– 226.
    • (1996) ACM Transactions on Mathematical Software , vol.22 , pp. 187-226
    • Duff, I.S.1    Reid, J.K.2
  • 100
    • 85098064726 scopus 로고    scopus 로고
    • Second order corrections for non-differentiable optimization, in Numerical Analysis, D. Griffiths, ed., Springer Verlag, 1982, pp. 85–114. Proceedings Dundee 1981
    • Second order corrections for non-differentiable optimization, in Numerical Analysis, D. Griffiths, ed., Springer Verlag, 1982, pp. 85–114. Proceedings Dundee 1981.
  • 101
    • 0003768769 scopus 로고
    • John Wiley & Sons, New York, second ed
    • , Practical Methods of Optimization, John Wiley & Sons, New York, second ed., 1987.
    • (1987) Practical Methods of Optimization
  • 102
    • 0043176711 scopus 로고
    • An optimal positive definite update for sparse Hessian matrices
    • ), pp
    • , An optimal positive definite update for sparse Hessian matrices, SIAM Journal on Optimization, 5 (1995), pp. 192–218.
    • (1995) SIAM Journal on Optimization , vol.5 , pp. 192-218
  • 103
    • 19844383895 scopus 로고    scopus 로고
    • Stable reduced hessian updates for indefinite quadratic programming
    • ), pp
    • , Stable reduced hessian updates for indefinite quadratic programming, Mathematical Programming, 87 (2000), pp. 251–264.
    • (2000) Mathematical Programming , vol.87 , pp. 251-264
  • 105
    • 0001556338 scopus 로고    scopus 로고
    • Nonlinear programming without a penalty function
    • ), pp
    • R. FLETCHER AND S. LEYFFER, Nonlinear programming without a penalty function, Mathematical Programming, Series A, 91 (2002), pp. 239–269.
    • (2002) Mathematical Programming, Series A , vol.91 , pp. 239-269
    • Fletcher, R.1    Leyffer, S.2
  • 107
    • 0000615669 scopus 로고
    • Function minimization by conjugate gradients
    • ), pp
    • R. FLETCHER AND C. M. REEVES, Function minimization by conjugate gradients, Computer Journal, 7 (1964), pp. 149–154.
    • (1964) Computer Journal , vol.7 , pp. 149-154
    • Fletcher, R.1    Reeves, C.M.2
  • 108
    • 34249970002 scopus 로고
    • Nonlinear programming and nonsmooth optimization by successive linear programming
    • ), pp
    • R. FLETCHER AND E. SAINZ DE LA MAZA, Nonlinear programming and nonsmooth optimization by successive linear programming, Mathematical Programming, 43 (1989), pp. 235–256.
    • (1989) Mathematical Programming , vol.43 , pp. 235-256
    • Fletcher, R.1    Sainz De La Maza, E.2
  • 109
    • 85098052446 scopus 로고
    • Recent Advances in Global Optimization, Princeton University Press, Princeton
    • C. FLOUDAS AND P. PARDALOS, eds
    • C. FLOUDAS AND P. PARDALOS, eds., Recent Advances in Global Optimization, Princeton University Press, Princeton, NJ, 1992.
    • (1992) NJ
  • 110
    • 0000433309 scopus 로고
    • Updated triangular factors of the basis to maintain sparsity in the product form simplex method
    • ), pp
    • J. J. H. FORREST AND J. A. TOMLIN, Updated triangular factors of the basis to maintain sparsity in the product form simplex method, Mathematical Programming, 2 (1972), pp. 263–278.
    • (1972) Mathematical Programming , vol.2 , pp. 263-278
    • Forrest, J.J.H.1    Tomlin, J.A.2
  • 111
    • 0036959271 scopus 로고    scopus 로고
    • Interior methods for nonlinear optimization
    • ), pp
    • A. FORSGREN, P. E. GILL, AND M. H. WRIGHT, Interior methods for nonlinear optimization, SIAM Review, 44 (2003), pp. 525–597.
    • (2003) SIAM Review , vol.44 , pp. 525-597
    • Forsgren, A.1    Gill, P.E.2    Wright, M.H.3
  • 113
    • 0002189178 scopus 로고
    • Solving symmetric indefinite systems in an interior-point method for linear programming
    • ), pp
    • R. FOURER AND S. MEHROTRA, Solving symmetric indefinite systems in an interior-point method for linear programming, Mathematical Programming, 62 (1993), pp. 15–39.
    • (1993) Mathematical Programming , vol.62 , pp. 15-39
    • Fourer, R.1    Mehrotra, S.2
  • 114
    • 19844373567 scopus 로고    scopus 로고
    • A globally convergent linearly constrained Lagrangian method for nonlinear optimization
    • ), pp
    • M. P. FRIEDLANDER AND M. A. SAUNDERS, A globally convergent linearly constrained Lagrangian method for nonlinear optimization, SIAM Journal on Optimization, 15 (2005), pp. 863–897.
    • (2005) SIAM Journal on Optimization , vol.15 , pp. 863-897
    • Friedlander, M.P.1    Saunders, M.A.2
  • 116
    • 0001837582 scopus 로고
    • Reduced quasi-Newton methods with feasibility improvement for nonlinearly constrained optimization
    • ), pp
    • D. GABAY, Reduced quasi-Newton methods with feasibility improvement for nonlinearly constrained optimization, Mathematical Programming Studies, 16 (1982), pp. 18–44.
    • (1982) Mathematical Programming Studies , vol.16 , pp. 18-44
    • Gabay, D.1
  • 117
    • 0016987048 scopus 로고
    • Superlinearly convergent quasi-Newton methods for nonlinearly constrained optimization problems
    • ), pp
    • U. M. GARCIA-PALOMARES AND O. L. MANGASARIAN, Superlinearly convergent quasi-Newton methods for nonlinearly constrained optimization problems, Mathematical Programming, 11 (1976), pp. 1–13.
    • (1976) Mathematical Programming , vol.11 , pp. 1-13
    • Garcia-Palomares, U.M.1    Mangasarian, O.L.2
  • 118
    • 30244491763 scopus 로고    scopus 로고
    • More AD of nonlinear AMPL models: Computing Hessian information and exploiting partial separability
    • M. Berz, C. Bischof, G. F. Corliss, and A. Griewank, eds., SIAM Publications, Philadelphia, PA, pp
    • D. M. GAY, More AD of nonlinear AMPL models: computing Hessian information and exploiting partial separability, in Computational Differentiation: Techniques, Applications, and Tools, M. Berz, C. Bischof, G. F. Corliss, and A. Griewank, eds., SIAM Publications, Philadelphia, PA, 1996, pp. 173–184.
    • (1996) Computational Differentiation: Techniques, Applications, and Tools , pp. 173-184
    • Gay, D.M.1
  • 119
    • 0020831469 scopus 로고
    • The convergence of variable metric matrices in unconstrained optimization
    • ), pp
    • R.-P. GE AND M. J. D. POWELL, The convergence of variable metric matrices in unconstrained optimization, Mathematical Programming, 27 (1983), pp. 123–143.
    • (1983) Mathematical Programming , vol.27 , pp. 123-143
    • Ge, R.-P.1    Powell, M.J.D.2
  • 120
    • 28244465516 scopus 로고    scopus 로고
    • What color is your Jacobian? Graph coloring for computing derivatives
    • ), pp
    • A. H. GEBREMEDHIN, F. MANNE, AND A. POTHEN, What color is your Jacobian? Graph coloring for computing derivatives, SIAM Review, 47 (2005), pp. 629–705.
    • (2005) SIAM Review , vol.47 , pp. 629-705
    • Gebremedhin, A.H.1    Manne, F.2    Pothen, A.3
  • 122
    • 34249975203 scopus 로고
    • Some numerical experiments with variable-storage quasi-Newton algorithms
    • ), pp
    • J. GILBERT AND C. LEMARÉCHAL, Some numerical experiments with variable-storage quasi-Newton algorithms, Mathematical Programming, Series B, 45 (1989), pp. 407–435.
    • (1989) Mathematical Programming, Series B , vol.45 , pp. 407-435
    • Gilbert, J.1    Lemaréchal, C.2
  • 123
    • 0002824920 scopus 로고
    • Global convergence properties of conjugate gradient methods for optimization
    • ), pp
    • J. GILBERT AND J. NOCEDAL, Global convergence properties of conjugate gradient methods for optimization, SIAM Journal on Optimization, 2 (1992), pp. 21–42.
    • (1992) SIAM Journal on Optimization , vol.2 , pp. 21-42
    • Gilbert, J.1    Nocedal, J.2
  • 125
    • 2442519470 scopus 로고    scopus 로고
    • Limited-memory reduced-Hessian methods for unconstrained optimization
    • ), pp
    • P. E. GILL AND M. W. LEONARD, Limited-memory reduced-Hessian methods for unconstrained optimization, SIAM Journal on Optimization, 14 (2003), pp. 380–401.
    • (2003) SIAM Journal on Optimization , vol.14 , pp. 380-401
    • Gill, P.E.1    Leonard, M.W.2
  • 126
    • 0001596694 scopus 로고
    • Numerically stable methods for quadratic programming
    • ), pp
    • P. E. GILL AND W. MURRAY, Numerically stable methods for quadratic programming, Mathematical Programming, 14 (1978), pp. 349–372.
    • (1978) Mathematical Programming , vol.14 , pp. 349-372
    • Gill, P.E.1    Murray, W.2
  • 127
    • 19944403455 scopus 로고    scopus 로고
    • User’s guide for SNOPT (Version 5.3): A FOR-TRAN package for large-scale nonlinear programming
    • Department of Mathematics, University of California, San Diego
    • P. E. GILL, W. MURRAY, AND M. A. SAUNDERS, User’s guide for SNOPT (Version 5.3): A FOR-TRAN package for large-scale nonlinear programming, Technical Report NA 97-4, Department of Mathematics, University of California, San Diego, 1997.
    • (1997) Technical Report NA , vol.97-4
    • Gill, P.E.1    Murray, W.2    Saunders, M.A.3
  • 128
    • 0036433588 scopus 로고    scopus 로고
    • SNOPT: An SQP algorithm for large-scale constrained optimization
    • ), pp
    • , SNOPT: An SQP algorithm for large-scale constrained optimization, SIAM Journal on Optimization, 12 (2002), pp. 979–1006.
    • (2002) SIAM Journal on Optimization , vol.12 , pp. 979-1006
  • 131
    • 85065363369 scopus 로고
    • Redwood City, California
    • , Numerical Linear Algebra and Optimization, Vol. 1, Addison Wesley, Redwood City, California, 1991.
    • (1991) Addison Wesley
  • 132
    • 0018925055 scopus 로고
    • Curvilinear path steplength algorithms for minimization which use directions of negative curvature
    • ), pp
    • D. GOLDFARB, Curvilinear path steplength algorithms for minimization which use directions of negative curvature, Mathematical Programming, 18 (1980), pp. 31–40.
    • (1980) Mathematical Programming , vol.18 , pp. 31-40
    • Goldfarb, D.1
  • 133
    • 20944450471 scopus 로고
    • Steepest edge simplex algorithms for linear programming
    • ), pp
    • D. GOLDFARB AND J. FORREST, Steepest edge simplex algorithms for linear programming, Mathematical Programming, 57 (1992), pp. 341–374.
    • (1992) Mathematical Programming , vol.57 , pp. 341-374
    • Goldfarb, D.1    Forrest, J.2
  • 134
    • 0000726097 scopus 로고
    • A practicable steepest-edge simplex algorithm
    • ), pp
    • D. GOLDFARB AND J. K. REID, A practicable steepest-edge simplex algorithm, Mathematical Programming, 12 (1977), pp. 361–373.
    • (1977) Mathematical Programming , vol.12 , pp. 361-373
    • Goldfarb, D.1    Reid, J.K.2
  • 135
    • 0024631560 scopus 로고
    • Some history of the conjugate gradient methods and the Lanczos algorithms: 1948–1976
    • ), pp
    • G. GOLUB AND D. O’LEARY, Some history of the conjugate gradient methods and the Lanczos algorithms: 1948–1976, SIAM Review, 31 (1989), pp. 50–100.
    • (1989) SIAM Review , vol.31 , pp. 50-100
    • Golub, G.1    O’Leary, D.2
  • 136
    • 0004236492 scopus 로고    scopus 로고
    • The Johns Hopkins University Press, Baltimore, third ed
    • G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, The Johns Hopkins University Press, Baltimore, third ed., 1996.
    • (1996) Matrix Computations
  • 137
    • 0029358316 scopus 로고
    • HOPDM (Version 2.12): A fast LP solver based on a primal-dual interior point method
    • ), pp
    • J. GONDZIO, HOPDM (version 2.12): A fast LP solver based on a primal-dual interior point method, European Journal of Operations Research, 85 (1995), pp. 221–225.
    • (1995) European Journal of Operations Research , vol.85 , pp. 221-225
    • Gondzio, J.1
  • 138
    • 0030242781 scopus 로고    scopus 로고
    • Multiple centrality corrections in a primal-dual method for linear programming
    • ), pp
    • , Multiple centrality corrections in a primal-dual method for linear programming, Computational Optimization and Applications, 6 (1996), pp. 137–156.
    • (1996) Computational Optimization and Applications , vol.6 , pp. 137-156
  • 140
    • 0001087725 scopus 로고
    • On the accurate determination of search directions for simple differentiable penalty functions
    • ), pp
    • N. I. M. GOULD, On the accurate determination of search directions for simple differentiable penalty functions, I.M.A. Journal on Numerical Analysis, 6 (1986), pp. 357–372.
    • (1986) I.M.A. Journal on Numerical Analysis , vol.6 , pp. 357-372
    • Gould, N.I.M.1
  • 141
    • 0000976514 scopus 로고
    • On the convergence of a sequential penalty function method for constrained minimization
    • ), pp
    • , On the convergence of a sequential penalty function method for constrained minimization, SIAM Journal on Numerical Analysis, 26 (1989), pp. 107–128.
    • (1989) SIAM Journal on Numerical Analysis , vol.26 , pp. 107-128
  • 142
    • 0346672928 scopus 로고
    • An algorithm for large scale quadratic programming
    • ), pp
    • , An algorithm for large scale quadratic programming, I.M.A. Journal on Numerical Analysis, 11 (1991), pp. 299–324.
    • (1991) I.M.A. Journal on Numerical Analysis , vol.11 , pp. 299-324
  • 143
    • 0036344992 scopus 로고    scopus 로고
    • On the solution of equality constrained quadratic problems arising in optimization
    • ), pp
    • N. I. M. GOULD, M. E. HRIBAR, AND J. NOCEDAL, On the solution of equality constrained quadratic problems arising in optimization, SIAM Journal on Scientific Computing, 23 (2001), pp. 1375– 1394.
    • (2001) SIAM Journal on Scientific Computing , vol.23 , pp. 1375-1394
    • Gould, N.I.M.1    Hribar, M.E.2    Nocedal, J.3
  • 144
    • 14944339092 scopus 로고    scopus 로고
    • A multidimensional filter algorithm for nonlinear equations and nonlinear least squares
    • ), pp
    • N.I.M. GOULD, S. LEYFFER, AND P. L. TOINT, A multidimensional filter algorithm for nonlinear equations and nonlinear least squares, SIAM Journal on Optimization, 15 (2004), pp. 17–38.
    • (2004) SIAM Journal on Optimization , vol.15 , pp. 17-38
    • Gould, N.I.M.1    Leyffer, S.2    Toint, P.L.3
  • 145
  • 146
    • 2442619389 scopus 로고    scopus 로고
    • GALAHAD—a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization
    • ), pp
    • N. I. M. GOULD, D. ORBAN, AND P. L. TOINT, GALAHAD—a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization, ACM Transactions on Mathematical Software, 29 (2003), pp. 353–372.
    • (2003) ACM Transactions on Mathematical Software , vol.29 , pp. 353-372
    • Gould, N.I.M.1    Orban, D.2    Toint, P.L.3
  • 147
    • 19844363263 scopus 로고    scopus 로고
    • Numerical methods for large-scale nonlinear optimization
    • ), pp
    • N. I. M. GOULD, D. ORBAN, AND P. L. TOINT, Numerical methods for large-scale nonlinear optimization, Acta Numerica, 14 (2005), pp. 299–361.
    • (2005) Acta Numerica , vol.14 , pp. 299-361
    • Gould, N.I.M.1    Orban, D.2    Toint, P.L.3
  • 148
    • 0036776431 scopus 로고    scopus 로고
    • An iterative working-set method for large-scale non-convex quadratic programming
    • ), pp
    • N. I. M. GOULD AND P. L. TOINT, An iterative working-set method for large-scale non-convex quadratic programming, Applied Numerical Mathematics, 43 (2002), pp. 109–128.
    • (2002) Applied Numerical Mathematics , vol.43 , pp. 109-128
    • Gould, N.I.M.1    Toint, P.L.2
  • 149
    • 2442517922 scopus 로고    scopus 로고
    • Numerical methods for large-scale non-convex quadratic programming
    • A. H. Siddiqi and M. Kočvara, eds., Dordrecht, The Netherlands, Kluwer Academic Publishers, pp
    • , Numerical methods for large-scale non-convex quadratic programming, in Trends in Industrial and Applied Mathematics, A. H. Siddiqi and M. Kočvara, eds., Dordrecht, The Netherlands, 2002, Kluwer Academic Publishers, pp. 149–179.
    • (2002) Trends in Industrial and Applied Mathematics , pp. 149-179
  • 150
    • 0026858844 scopus 로고
    • Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation
    • ), pp
    • A. GRIEWANK, Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation, Optimization Methods and Software, 1 (1992), pp. 35–54.
    • (1992) Optimization Methods and Software , vol.1 , pp. 35-54
    • Griewank, A.1
  • 151
    • 85098047499 scopus 로고
    • Automatic directional differentiation of nonsmooth composite functions
    • , Automatic directional differentiation of nonsmooth composite functions, in Seventh French-German Conference on Optimization, 1994.
    • (1994) Seventh French-German Conference on Optimization
  • 152
    • 0003319841 scopus 로고    scopus 로고
    • Principles and Techniques of Automatic Differentiation, vol. 19 of Frontiers in Applied Mathematics
    • A. GRIEWANK, Evaluating Derivatives: Principles and Techniques of Automatic Differentiation, vol. 19 of Frontiers in Applied Mathematics, SIAM, 2000.
    • (2000) SIAM
    • Griewank, A.1    Derivatives, E.2
  • 153
    • 0003688299 scopus 로고
    • SIAM Publications, Philadelphia, Penn
    • A. GRIEWANK AND G. F. CORLISS, eds., Automatic Differentition of Algorithms, SIAM Publications, Philadelphia, Penn., 1991.
    • (1991) Automatic Differentition of Algorithms
  • 154
    • 0030168036 scopus 로고    scopus 로고
    • AND J. UTKE, ADOL-C, A package for the automatic differentiation of algorithms written in C/C++
    • ), pp
    • A. GRIEWANK, D. JUEDES, AND J. UTKE, ADOL-C, A package for the automatic differentiation of algorithms written in C/C++, ACM Transactions on Mathematical Software, 22 (1996), pp. 131–167.
    • (1996) ACM Transactions on Mathematical Software , vol.22 , pp. 131-167
    • Griewank, A.1    Juedes, D.2
  • 155
    • 0000782630 scopus 로고
    • Local convergence analysis of partitioned quasi-Newton updates
    • ), pp
    • A. GRIEWANK AND P. L. TOINT, Local convergence analysis of partitioned quasi-Newton updates, Numerische Mathematik, 39 (1982), pp. 429–448.
    • (1982) Numerische Mathematik , vol.39 , pp. 429-448
    • Griewank, A.1    Toint, P.L.2
  • 156
    • 0013358480 scopus 로고
    • Partitioned variable metric updates for large structured optimization problems
    • ), pp
    • , Partitioned variable metric updates for large structured optimization problems, Numerische Mathematik, 39 (1982), pp. 119–137.
    • (1982) Numerische Mathematik , vol.39 , pp. 119-137
  • 157
    • 0002523847 scopus 로고    scopus 로고
    • Optimal time and minimum space time product for reversing a certain class of programs
    • Tools, M. Berz, C. Bischof, G. Corliss, and A. Griewank, eds., SIAM, Philadelphia, pp
    • J. GRIMM, L. POTTIER, AND N. ROSTAING-SCHMIDT, Optimal time and minimum space time product for reversing a certain class of programs, in Computational Differentiation, Techniques, Applications, and Tools, M. Berz, C. Bischof, G. Corliss, and A. Griewank, eds., SIAM, Philadelphia, 1996, pp. 95–106.
    • (1996) Computational Differentiation, Techniques, Applications, And , pp. 95-106
    • Grimm, J.1    Pottier, L.2    Rostaing-Schmidt, N.3
  • 160
    • 0036347958 scopus 로고    scopus 로고
    • Minimizing a quadratic over a sphere
    • ), pp
    • W. W. HAGER, Minimizing a quadratic over a sphere, SIAM Journal on Optimization, 12 (2001), pp. 188–208.
    • (2001) SIAM Journal on Optimization , vol.12 , pp. 188-208
    • Hager, W.W.1
  • 161
    • 33144465578 scopus 로고    scopus 로고
    • A new conjugate gradient method with guaranteed descent and an efficient line search
    • ), pp
    • W. W. HAGER AND H. ZHANG, A new conjugate gradient method with guaranteed descent and an efficient line search, SIAM Journal on Optimization, 16 (2005), pp. 170–192.
    • (2005) SIAM Journal on Optimization , vol.16 , pp. 170-192
    • Hager, W.W.1    Zhang, H.2
  • 162
    • 85098093630 scopus 로고    scopus 로고
    • A survey of nonlinear conjugate gradient methods
    • To appear in
    • , A survey of nonlinear conjugate gradient methods. To appear in the Pacific Journal of Optimization, 2005.
    • (2005) The Pacific Journal of Optimization
  • 163
    • 0000373474 scopus 로고
    • Superlinearly convergent variable metric algorithms for general nonlinear programming problems
    • ), pp
    • S. P. HAN, Superlinearly convergent variable metric algorithms for general nonlinear programming problems, Mathematical Programming, 11 (1976), pp. 263–282.
    • (1976) Mathematical Programming , vol.11 , pp. 263-282
    • Han, S.P.1
  • 164
    • 34250293137 scopus 로고
    • A globally convergent method for nonlinear programming
    • ), pp
    • , A globally convergent method for nonlinear programming, Journal of Optimization Theory and Applications, 22 (1977), pp. 297–309.
    • (1977) Journal of Optimization Theory and Applications , vol.22 , pp. 297-309
  • 165
    • 34250270048 scopus 로고
    • Exact penalty functions in nonlinear programming
    • ), pp
    • S. P. HAN AND O. L. MANGASARIAN, Exact penalty functions in nonlinear programming, Mathematical Programming, 17 (1979), pp. 251–269.
    • (1979) Mathematical Programming , vol.17 , pp. 251-269
    • Han, S.P.1    Mangasarian, O.L.2
  • 171
    • 0036207607 scopus 로고    scopus 로고
    • Asynchronous parallel pattern search for nonlinear optimization
    • ), pp
    • P. HOUGH, T. KOLDA, AND V. TORCZON, Asynchronous parallel pattern search for nonlinear optimization, SIAM Journal on Optimization, 23 (2001), pp. 134–156.
    • (2001) SIAM Journal on Optimization , vol.23 , pp. 134-156
    • Hough, P.1    Kolda, T.2    Torczon, V.3
  • 175
    • 51249181779 scopus 로고
    • A new polynomial-time algorithm for linear programming
    • ), pp
    • N. KARMARKAR, A new polynomial-time algorithm for linear programming, Combinatorics, 4 (1984), pp. 373–395.
    • (1984) Combinatorics , vol.4 , pp. 373-395
    • Karmarkar, N.1
  • 178
    • 0033274347 scopus 로고    scopus 로고
    • Detection and remediation of stagnation in the Nelder-Mead algorithm using a sufficient decrease condition
    • ), pp
    • C. T. KELLEY, Detection and remediation of stagnation in the Nelder-Mead algorithm using a sufficient decrease condition, SIAM Journal on Optimization, 10 (1999), pp. 43–55.
    • (1999) SIAM Journal on Optimization , vol.10 , pp. 43-55
    • Kelley, C.T.1
  • 179
    • 85098076993 scopus 로고    scopus 로고
    • SIAM Publications, Philadelphia, PA
    • , Iterative Methods for Optimization, no. 18 in Frontiers in Applied Mathematics, SIAM Publications, Philadelphia, PA, 1999.
    • (1999) 18 in Frontiers in Applied Mathematics
  • 180
    • 0000564361 scopus 로고
    • A polynomial algorithm in linear programming
    • ), pp
    • L. G. KHACHIYAN, A polynomial algorithm in linear programming, Soviet Mathematics Doklady, 20 (1979), pp. 191–194.
    • (1979) Soviet Mathematics Doklady , vol.20 , pp. 191-194
    • Khachiyan, L.G.1
  • 181
    • 0002450905 scopus 로고
    • A theoretical and experimental study of the symmetric rank one update
    • ), pp
    • H. F. KHALFAN, R. H. BYRD, AND R. B. SCHNABEL, A theoretical and experimental study of the symmetric rank one update, SIAM Journal on Optimization, 3 (1993), pp. 1–24.
    • (1993) SIAM Journal on Optimization , vol.3 , pp. 1-24
    • Khalfan, H.F.1    Byrd, R.H.2    Schnabel, R.B.3
  • 182
    • 0001849163 scopus 로고
    • How good is the simplex algorithm?
    • O. Shisha, ed., Academic Press, New York, pp
    • V. KLEE AND G. J. MINTY, How good is the simplex algorithm? in Inequalities, O. Shisha, ed., Academic Press, New York, 1972, pp. 159–175.
    • (1972) Inequalities , pp. 159-175
  • 183
    • 0242667172 scopus 로고    scopus 로고
    • Optimization by direct search: New perspectives on some classical and modern methods
    • ), pp
    • T. G. KOLDA, R. M. LEWIS, AND V. TORCZON, Optimization by direct search: New perspectives on some classical and modern methods, SIAM Review, 45 (2003), pp. 385–482.
    • (2003) SIAM Review , vol.45 , pp. 385-482
    • Kolda, T.G.1    Lewis, R.M.2    Torczon, V.3
  • 184
    • 0041844993 scopus 로고    scopus 로고
    • PENNON, a code for nonconvex nonlinear and semidefinite programming
    • ), pp
    • M. KOČVARA AND M. STINGL, PENNON, a code for nonconvex nonlinear and semidefinite programming, Optimization Methods and Software, 18 (2003), pp. 317–333.
    • (2003) Optimization Methods and Software , vol.18 , pp. 317-333
    • Kočvara, M.1    Stingl, M.2
  • 186
    • 0032251894 scopus 로고    scopus 로고
    • Convergence properties of the Nelder-Mead simplex algorithm in low dimensions
    • ), pp
    • J. W. LAGARIAS, J. A. REEDS, M. H. WRIGHT, AND P. E. WRIGHT, Convergence properties of the Nelder-Mead simplex algorithm in low dimensions, SIAM Journal on Optimization, 9 (1998), pp. 112–147.
    • (1998) SIAM Journal on Optimization , vol.9 , pp. 112-147
    • Lagarias, J.W.1    Reeds, J.A.2    Wright, M.H.3    Wright, P.E.4
  • 187
    • 0003655414 scopus 로고
    • Addison-Wesley, Reading, MA, second ed
    • S. LANG, Real Analysis, Addison-Wesley, Reading, MA, second ed., 1983.
    • (1983) Real Analysis
    • Lang, S.1
  • 189
    • 85098067931 scopus 로고    scopus 로고
    • C. LEMARÉCHAL, A view of line searches, in Optimization and Optimal Control, W. Oettli and J. Stoer, eds., no. 30 in Lecture Notes in Control and Information Science, Springer-Verlag, 1981, pp. 59–78
    • C. LEMARÉCHAL, A view of line searches, in Optimization and Optimal Control, W. Oettli and J. Stoer, eds., no. 30 in Lecture Notes in Control and Information Science, Springer-Verlag, 1981, pp. 59–78.
  • 190
    • 0000873069 scopus 로고
    • A method for the solution of certain non-linear problems in least squares
    • ), pp
    • K. LEVENBERG, A method for the solution of certain non-linear problems in least squares, Quarterly of Applied Mathematics, 2 (1944), pp. 164–168.
    • (1944) Quarterly of Applied Mathematics , vol.2 , pp. 164-168
    • Levenberg, K.1
  • 191
    • 85098065135 scopus 로고    scopus 로고
    • G. LOPEZ-CALVA, AND J. NOCEDAL, Interior methods for mathematical programs with complementarity constraints
    • Optimization Technology Center, Northwestern University, Evanston, IL
    • S. LEYFFER, G. LOPEZ-CALVA, AND J. NOCEDAL, Interior methods for mathematical programs with complementarity constraints, technical report 8, Optimization Technology Center, Northwestern University, Evanston, IL, 2004.
    • (2004) Technical Report , vol.8
    • Leyffer, S.1
  • 192
    • 0033436056 scopus 로고    scopus 로고
    • Newton’s method for large bound-constrained optimization problems
    • ), pp
    • C. LIN AND J. MORÉ, Newton’s method for large bound-constrained optimization problems, SIAM Journal on Optimization, 9 (1999), pp. 1100–1127.
    • (1999) SIAM Journal on Optimization , vol.9 , pp. 1100-1127
    • Lin, C.1    Moré, J.2
  • 193
    • 0033294627 scopus 로고    scopus 로고
    • Incomplete Cholesky factorizations with limited memory
    • ), pp
    • C. LIN AND J. J. MORÉ, Incomplete Cholesky factorizations with limited memory, SIAM Journal on Scientific Computing, 21 (1999), pp. 24–45.
    • (1999) SIAM Journal on Scientific Computing , vol.21 , pp. 24-45
    • Lin, C.1    Moré, J.J.2
  • 194
    • 33646887390 scopus 로고
    • On the limited-memory BFGS method for large scale optimization
    • ), pp
    • D. C. LIU AND J. NOCEDAL, On the limited-memory BFGS method for large scale optimization, Mathematical Programming, 45 (1989), pp. 503–528.
    • (1989) Mathematical Programming , vol.45 , pp. 503-528
    • Liu, D.C.1    Nocedal, J.2
  • 196
    • 0345293940 scopus 로고    scopus 로고
    • Indefinitely preconditioned inexact Newton method for large sparse equality constrained nonlinear programming problems
    • ), pp
    • L. LUKŠAN AND J. VLČEK, Indefinitely preconditioned inexact Newton method for large sparse equality constrained nonlinear programming problems, Numerical Linear Algebra with Applications, 5 (1998), pp. 219–247.
    • (1998) Numerical Linear Algebra with Applications , vol.5 , pp. 219-247
    • Lukšan, L.1    Vlček, J.2
  • 198
    • 0003775298 scopus 로고
    • McGraw-Hill, New York, Reprinted by SIAM Publications
    • O. L. MANGASARIAN, Nonlinear Programming, McGraw-Hill, New York, 1969. Reprinted by SIAM Publications, 1995.
    • (1969) Nonlinear Programming , pp. 1995
    • Mangasarian, O.L.1
  • 200
    • 0013238081 scopus 로고    scopus 로고
    • Wedge trust region methods for derivative free optimization
    • ), pp
    • M. MARAZZI AND J. NOCEDAL, Wedge trust region methods for derivative free optimization, Mathematical Programming, Series A, 91 (2002), pp. 289–305.
    • (2002) Mathematical Programming, Series A , vol.91 , pp. 289-305
    • Marazzi, M.1    Nocedal, J.2
  • 201
    • 84995186518 scopus 로고
    • Portfolio selection
    • ), pp
    • H. M. MARKOWITZ, Portfolio selection, Journal of Finance, 8 (1952), pp. 77–91.
    • (1952) Journal of Finance , vol.8 , pp. 77-91
    • Markowitz, H.M.1
  • 202
    • 0000444373 scopus 로고
    • The elimination form of the inverse and its application to linear programming
    • ), pp
    • , The elimination form of the inverse and its application to linear programming, Management Science, 3 (1957), pp. 255–269.
    • (1957) Management Science , vol.3 , pp. 255-269
  • 203
    • 0000169232 scopus 로고
    • An algorithm for least squares estimation of non-linear parameters
    • ), pp
    • D. W. MARQUARDT, An algorithm for least squares estimation of non-linear parameters, SIAM Journal, 11 (1963), pp. 431–441.
    • (1963) SIAM Journal , vol.11 , pp. 431-441
    • Marquardt, D.W.1
  • 204
    • 0002897657 scopus 로고
    • A superlinearly convergent algorithm for constrained optimization problems
    • ), pp
    • D. Q. MAYNE AND E. POLAK, A superlinearly convergent algorithm for constrained optimization problems, Mathematical Programming Studies, 16 (1982), pp. 45–61.
    • (1982) Mathematical Programming Studies , vol.16 , pp. 45-61
    • Mayne, D.Q.1    Polak, E.2
  • 205
    • 84972492753 scopus 로고
    • An analogue of Moreau’s proximation theorem, with applications to the nonlinear complementarity problem
    • ), pp
    • L. MCLINDEN, An analogue of Moreau’s proximation theorem, with applications to the nonlinear complementarity problem, Pacific Journal of Mathematics, 88 (1980), pp. 101–161.
    • (1980) Pacific Journal of Mathematics , vol.88 , pp. 101-161
    • McLinden, L.1
  • 206
    • 0001961709 scopus 로고    scopus 로고
    • Pathways to the optimal set in linear programming, in Progress in Mathematical Programming: Interior-Point and Related Methods, N. Megiddo, ed., Springer-Verlag, New York
    • pp
    • N. MEGIDDO, Pathways to the optimal set in linear programming, in Progress in Mathematical Programming: Interior-Point and Related Methods, N. Megiddo, ed., Springer-Verlag, New York, NY, 1989, ch. 8, pp. 131–158.
    • NY, 1989, Ch , vol.8 , pp. 131-158
    • Megiddo, N.1
  • 207
    • 0000561116 scopus 로고
    • On the implementation of a primal-dual interior point method
    • ), pp
    • S. MEHROTRA, On the implementation of a primal-dual interior point method, SIAM Journal on Optimization, 2 (1992), pp. 575–601.
    • (1992) SIAM Journal on Optimization , vol.2 , pp. 575-601
    • Mehrotra, S.1
  • 208
    • 0000836925 scopus 로고
    • On adaptive step primal-dual interior-point algorithms for linear programming
    • ), pp
    • S. MIZUNO, M. TODD, AND Y. YE, On adaptive step primal-dual interior-point algorithms for linear programming, Mathematics of Operations Research, 18 (1993), pp. 964–981.
    • (1993) Mathematics of Operations Research , vol.18 , pp. 964-981
    • Mizuno, S.1    Todd, M.2    Ye, Y.3
  • 209
    • 0034345411 scopus 로고    scopus 로고
    • Automatic preconditioning by limited memory quasi-newton updating
    • ), pp
    • J. L. MORALES AND J. NOCEDAL, Automatic preconditioning by limited memory quasi-newton updating, SIAM Journal on Optimization, 10 (2000), pp. 1079–1096.
    • (2000) SIAM Journal on Optimization , vol.10 , pp. 1079-1096
    • Morales, J.L.1    Nocedal, J.2
  • 211
    • 85098078677 scopus 로고
    • Recent developments in algorithms and software for trust region methods, in Mathematical Programming: The State of the Art, Springer-Verlag, Berlin, pp
    • , Recent developments in algorithms and software for trust region methods, in Mathematical Programming: The State of the Art, Springer-Verlag, Berlin, 1983, pp. 258–287.
    • (1983) , pp. 258-287
  • 212
    • 85098094964 scopus 로고
    • A collection of nonlinear model problems, in Computational Solution of Nonlinear Systems of Equations, vol. 26 of Lectures in Applied Mathematics, American Mathematical Society, Providence, RI, pp
    • , A collection of nonlinear model problems, in Computational Solution of Nonlinear Systems of Equations, vol. 26 of Lectures in Applied Mathematics, American Mathematical Society, Providence, RI, 1990, pp. 723–762.
    • (1990) , pp. 723-762
  • 213
    • 0001818862 scopus 로고
    • On the use of directions of negative curvature in a modified Newton method
    • ), pp
    • J. J. MORÉ AND D. C. SORENSEN, On the use of directions of negative curvature in a modified Newton method, Mathematical Programming, 16 (1979), pp. 1–20.
    • (1979) Mathematical Programming , vol.16 , pp. 1-20
    • Moré, J.J.1    Sorensen, D.C.2
  • 215
    • 85098059590 scopus 로고    scopus 로고
    • Newton’s method, in Studies in Numerical Analysis, vol. 24 of MAA Studies in Mathematics, The Mathematical Association of America, 1984, pp. 29–82
    • , Newton’s method, in Studies in Numerical Analysis, vol. 24 of MAA Studies in Mathematics, The Mathematical Association of America, 1984, pp. 29–82.
  • 216
    • 0028511736 scopus 로고
    • Line search algorithms with guaranteed sufficient decrease
    • ), pp
    • J. J. MORÉ AND D. J. THUENTE, Line search algorithms with guaranteed sufficient decrease, ACM Transactions on Mathematical Software, 20 (1994), pp. 286–307.
    • (1994) ACM Transactions on Mathematical Software , vol.20 , pp. 286-307
    • Moré, J.J.1    Thuente, D.J.2
  • 217
    • 0003714659 scopus 로고
    • SIAM Publications, Philadelphia
    • J. J. MORÉ AND S. J. WRIGHT, Optimization Software Guide, SIAM Publications, Philadelphia, 1993.
    • (1993) Optimization Software Guide
  • 218
    • 85098070284 scopus 로고
    • Technical Report SOL-83-20R
    • B. A. MURTAGH AND M. A. SAUNDERS, MINOS 5.1 User’s guide, Technical Report SOL-83-20R, Stanford University, 1987.
    • (1987) Stanford University
  • 219
    • 38949154277 scopus 로고
    • Some NP-complete problems in quadratic and nonlinear programming
    • ), pp
    • K. G. MURTY AND S. N. KABADI, Some NP-complete problems in quadratic and nonlinear programming, Mathematical Programming, 19 (1987), pp. 200–212.
    • (1987) Mathematical Programming , vol.19 , pp. 200-212
    • Murty, K.G.1    Kabadi, S.N.2
  • 220
    • 0021481124 scopus 로고
    • Newton-type minimization via the Lanczos method
    • ), pp
    • S. G. NASH, Newton-type minimization via the Lanczos method, SIAM Journal on Numerical Analysis, 21 (1984), pp. 553–572.
    • (1984) SIAM Journal on Numerical Analysis , vol.21 , pp. 553-572
    • Nash, S.G.1
  • 221
    • 0032201832 scopus 로고    scopus 로고
    • SUMT (Revisited)
    • ), pp
    • , SUMT (Revisited), Operations Research, 46 (1998), pp. 763–775.
    • (1998) Operations Research , vol.46 , pp. 763-775
  • 222
    • 8344274741 scopus 로고    scopus 로고
    • Optimal accumulation of Jacobian matrices by elimination methods on the dual computational graph
    • ), pp
    • U. NAUMANN, Optimal accumulation of Jacobian matrices by elimination methods on the dual computational graph, Mathematical Programming, 99 (2004), pp. 399–421.
    • (2004) Mathematical Programming , vol.99 , pp. 399-421
    • Naumann, U.1
  • 223
    • 0000238336 scopus 로고
    • A simplex method for function minimization
    • ), pp
    • J. A. NELDER AND R. MEAD, A simplex method for function minimization, The Computer Journal, 8 (1965), pp. 308–313.
    • (1965) The Computer Journal , vol.8 , pp. 308-313
    • Nelder, J.A.1    Mead, R.2
  • 228
    • 84966262179 scopus 로고
    • Updating quasi-Newton matrices with limited storage
    • ), pp
    • J. NOCEDAL, Updating quasi-Newton matrices with limited storage, Mathematics of Computation, 35 (1980), pp. 773–782.
    • (1980) Mathematics of Computation , vol.35 , pp. 773-782
    • Nocedal, J.1
  • 229
    • 84972047841 scopus 로고
    • Theory of algorithms for unconstrained optimization
    • ), pp
    • , Theory of algorithms for unconstrained optimization, Acta Numerica, 1 (1992), pp. 199– 242.
    • (1992) Acta Numerica , vol.1 , pp. 199-242
  • 234
    • 0039943513 scopus 로고
    • LSQR: An algorithm for sparse linear equations and sparse least squares
    • ), pp
    • C. C. PAIGE AND M. A. SAUNDERS, LSQR: An algorithm for sparse linear equations and sparse least squares, ACM Transactions on Mathematical Software, 8 (1982), pp. 43–71.
    • (1982) ACM Transactions on Mathematical Software , vol.8 , pp. 43-71
    • Paige, C.C.1    Saunders, M.A.2
  • 236
    • 0003322639 scopus 로고    scopus 로고
    • Optimization: Algorithms and Consistent Approximations, no. 124 in Applied Mathematical Sciences
    • E. POLAK, Optimization: Algorithms and Consistent Approximations, no. 124 in Applied Mathematical Sciences, Springer, 1997.
    • (1997) Springer
    • Polak, E.1
  • 239
    • 0001008029 scopus 로고
    • An efficient method for finding the minimum of a function of several variables without calculating derivatives
    • ), pp
    • M. J. D. POWELL, An efficient method for finding the minimum of a function of several variables without calculating derivatives, Computer Journal, 91 (1964), pp. 155–162.
    • (1964) Computer Journal , vol.91 , pp. 155-162
    • Powell, M.J.D.1
  • 240
    • 0002380692 scopus 로고
    • in Optimization, R. Fletcher, ed., Academic Press, New York, NY, pp
    • , A method for nonlinear constraints in minimization problems, in Optimization, R. Fletcher, ed., Academic Press, New York, NY, 1969, pp. 283–298.
    • (1969) A Method for Nonlinear Constraints in Minimization Problems , pp. 283-298
  • 241
    • 85098058175 scopus 로고    scopus 로고
    • A hybrid method for nonlinear equations, in Numerical Methods for Nonlinear Algebraic Equations, P. Rabinowitz, ed., Gordon & Breach, London, 1970, pp. 87–114
    • , A hybrid method for nonlinear equations, in Numerical Methods for Nonlinear Algebraic Equations, P. Rabinowitz, ed., Gordon & Breach, London, 1970, pp. 87–114.
  • 243
    • 0001258795 scopus 로고
    • On search directions for minimization algorithms
    • ), pp
    • , On search directions for minimization algorithms, Mathematical Programming, 4 (1973), pp. 193–201.
    • (1973) Mathematical Programming , vol.4 , pp. 193-201
  • 244
    • 85098091080 scopus 로고    scopus 로고
    • Convergence properties of a class of minimization algorithms, in Nonlinear Programming 2, O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds., Academic Press, New York, 1975, pp. 1–27
    • , Convergence properties of a class of minimization algorithms, in Nonlinear Programming 2, O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds., Academic Press, New York, 1975, pp. 1–27.
  • 245
    • 0016990059 scopus 로고
    • Some convergence properties of the conjugate gradient method
    • ), pp
    • , Some convergence properties of the conjugate gradient method, Mathematical Programming, 11 (1976), pp. 42–49.
    • (1976) Mathematical Programming , vol.11 , pp. 42-49
  • 246
    • 85098072234 scopus 로고    scopus 로고
    • Some global convergence properties of a variable metric algorithm for minimization without exact line searches, in Nonlinear Programming, SIAM-AMS Proceedings, Vol. IX, R. W. Cottle and C. E. Lemke, eds., SIAM Publications, 1976, pp. 53–72
    • , Some global convergence properties of a variable metric algorithm for minimization without exact line searches, in Nonlinear Programming, SIAM-AMS Proceedings, Vol. IX, R. W. Cottle and C. E. Lemke, eds., SIAM Publications, 1976, pp. 53–72.
  • 247
    • 85098051620 scopus 로고    scopus 로고
    • A fast algorithm for nonlinearly constrained optimization calculations, in Numerical Analysis Dundee 1977, G. A. Watson, ed., Springer Verlag, Berlin, 1977, pp. 144–157
    • , A fast algorithm for nonlinearly constrained optimization calculations, in Numerical Analysis Dundee 1977, G. A. Watson, ed., Springer Verlag, Berlin, 1977, pp. 144–157.
  • 248
    • 33846446220 scopus 로고
    • Restart procedures for the conjugate gradient method
    • ), pp
    • , Restart procedures for the conjugate gradient method, Mathematical Programming, 12 (1977), pp. 241–254.
    • (1977) Mathematical Programming , vol.12 , pp. 241-254
  • 249
    • 0000406419 scopus 로고
    • Algorithms for nonlinear constraints that use Lagrangian functions
    • ), pp
    • , Algorithms for nonlinear constraints that use Lagrangian functions, Mathematical Programming, 14 (1978), pp. 224–248.
    • (1978) Mathematical Programming , vol.14 , pp. 224-248
  • 250
    • 85098079365 scopus 로고    scopus 로고
    • The convergence of variable metric methods for nonlinearly constrained optimization calculations, in Nonlinear Programming 3, Academic Press, New York and London, 1978, pp. 27–63
    • , The convergence of variable metric methods for nonlinearly constrained optimization calculations, in Nonlinear Programming 3, Academic Press, New York and London, 1978, pp. 27–63.
  • 251
    • 85098092820 scopus 로고    scopus 로고
    • On the rate of convergence of variable metric algorithms for unconstrained optimization, Technical Report DAMTP 1983/NA7, Department of Applied Mathematics and Theoretical Physics, Cambridge University, 1983
    • , On the rate of convergence of variable metric algorithms for unconstrained optimization, Technical Report DAMTP 1983/NA7, Department of Applied Mathematics and Theoretical Physics, Cambridge University, 1983.
  • 252
    • 85098072278 scopus 로고
    • Springer-Verlag, Berlin, pp
    • , Variable metric methods for constrained optimization, in Mathematical Programming: The State of the Art, Bonn, 1982, Springer-Verlag, Berlin, 1983, pp. 288–311.
    • (1983) The State of the Art, Bonn, 1982 , pp. 288-311
  • 253
    • 0001219541 scopus 로고
    • Nonconvex minimization calculations and the conjugate gradient method
    • ), pp
    • , Nonconvex minimization calculations and the conjugate gradient method, Lecture Notes in Mathematics, 1066 (1984), pp. 122–141.
    • (1984) Lecture Notes in Mathematics , vol.1066 , pp. 122-141
  • 254
    • 85098079838 scopus 로고    scopus 로고
    • The performance of two subroutines for constrained optimization on some difficult test problems, in Numerical Optimization, P. T. Boggs, R. H. Byrd, and R. B. Schnabel, eds., SIAM Publications, Philadelphia, 1984
    • , The performance of two subroutines for constrained optimization on some difficult test problems, in Numerical Optimization, P. T. Boggs, R. H. Byrd, and R. B. Schnabel, eds., SIAM Publications, Philadelphia, 1984.
  • 255
    • 0022915175 scopus 로고
    • Convergence properties of algorithms for nonlinear optimization
    • ), pp
    • , Convergence properties of algorithms for nonlinear optimization, SIAM Review, 28 (1986), pp. 487–500.
    • (1986) SIAM Review , vol.28 , pp. 487-500
  • 256
    • 85011436515 scopus 로고    scopus 로고
    • Direct search algorithms for optimization calculations
    • ), pp
    • , Direct search algorithms for optimization calculations, Acta Numerica, 7 (1998), pp. 287– 336.
    • (1998) Acta Numerica , vol.7 , pp. 287-336
  • 257
    • 0041711007 scopus 로고    scopus 로고
    • UOBYQA: Unconstrained optimization by quadratic approximation
    • ), pp
    • , UOBYQA: unconstrained optimization by quadratic approximation, Mathematical Programming, Series B, 92 (2002), pp. 555–582.
    • (2002) Mathematical Programming, Series B , vol.92 , pp. 555-582
  • 258
    • 3042652542 scopus 로고    scopus 로고
    • On trust-region methods for unconstrained minimization without derivatives
    • ), pp
    • , On trust-region methods for unconstrained minimization without derivatives, Mathematical Programming, 97 (2003), pp. 605–623.
    • (2003) Mathematical Programming , vol.97 , pp. 605-623
  • 259
    • 21044444302 scopus 로고    scopus 로고
    • Least Frobenius norm updating of quadratic models that satisfy interpolation conditions
    • ), pp
    • , Least Frobenius norm updating of quadratic models that satisfy interpolation conditions, Mathematical Programming, 100 (2004), pp. 183–215.
    • (2004) Mathematical Programming , vol.100 , pp. 183-215
  • 261
  • 263
    • 0031141179 scopus 로고    scopus 로고
    • A semidefinite framework for trust region subproblems with applications to large scale minimization
    • ), pp
    • F. RENDL AND H. WOLKOWICZ, A semidefinite framework for trust region subproblems with applications to large scale minimization, Mathematical Programming, 77 (1997), pp. 273–299.
    • (1997) Mathematical Programming , vol.77 , pp. 273-299
    • Rendl, F.1    Wolkowicz, H.2
  • 264
    • 0001126902 scopus 로고    scopus 로고
    • Circumventing storage limitations in variational data assimilation studies
    • ), pp
    • J. M. RESTREPO, G. K. LEAF, AND A. GRIEWANK, Circumventing storage limitations in variational data assimilation studies, SIAM Journal on Scientific Computing, 19 (1998), pp. 1586–1605.
    • (1998) SIAM Journal on Scientific Computing , vol.19 , pp. 1586-1605
    • Restrepo, J.M.1    Leaf, G.K.2    Griewank, A.3
  • 265
    • 20944449199 scopus 로고
    • On the rate of superlinear convergence of a class of variable metric methods
    • ), pp
    • K. RITTER, On the rate of superlinear convergence of a class of variable metric methods, Numerische Mathematik, 35 (1980), pp. 293–313.
    • (1980) Numerische Mathematik , vol.35 , pp. 293-313
    • Ritter, K.1
  • 266
    • 0000061021 scopus 로고
    • A quadratically convergent algorithm for general nonlinear programming problems
    • ), pp
    • S. M. ROBINSON, A quadratically convergent algorithm for general nonlinear programming problems, Mathematical Programming, 3 (1972), pp. 145–156.
    • (1972) Mathematical Programming , vol.3 , pp. 145-156
    • Robinson, S.M.1
  • 267
    • 0001782846 scopus 로고
    • Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear-programming algorithms
    • ), pp
    • , Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear-programming algorithms, Mathematical Programming, 7 (1974), pp. 1–16.
    • (1974) Mathematical Programming , vol.7 , pp. 1-16
  • 268
    • 0020165423 scopus 로고
    • Generalized equations and their solutions. Part II: Applications to nonlinear programming
    • ), pp
    • , Generalized equations and their solutions. Part II: Applications to nonlinear programming, Mathematical Programming Study, 19 (1982), pp. 200–221.
    • (1982) Mathematical Programming Study , vol.19 , pp. 200-221
  • 269
    • 34250427726 scopus 로고
    • The multiplier method of Hestenes and Powell applied to convex programming
    • ), pp
    • R. T. ROCKAFELLAR, The multiplier method of Hestenes and Powell applied to convex programming, Journal of Optimization Theory and Applications, 12 (1973), pp. 555–562.
    • (1973) Journal of Optimization Theory and Applications , vol.12 , pp. 555-562
    • Rockafellar, R.T.1
  • 270
    • 0027606675 scopus 로고
    • Lagrange multipliers and optimality
    • ), pp
    • , Lagrange multipliers and optimality, SIAM Review, 35 (1993), pp. 183–238.
    • (1993) SIAM Review , vol.35 , pp. 183-238
  • 271
    • 11744359666 scopus 로고
    • A gradient projection algorithm for nonlinear constraints
    • ed., Academic Press, London and New York, pp
    • J. B. ROSEN AND J. KREUSER, A gradient projection algorithm for nonlinear constraints, in Numerical Methods for Non-Linear Optimization, F. A. Lootsma, ed., Academic Press, London and New York, 1972, pp. 297–300.
    • (1972) Numerical Methods for Non-Linear Optimization, F. A. Lootsma , pp. 297-300
    • Rosen, J.B.1    Kreuser, J.2
  • 273
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving non-symmetric linear systems
    • ), pp
    • Y. SAAD AND M. SCHULTZ, GMRES: A generalized minimal residual algorithm for solving non-symmetric linear systems, SIAM Journal on Scientific and Statistical Computing, 7 (1986), pp. 856–869.
    • (1986) SIAM Journal on Scientific and Statistical Computing , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.2
  • 274
    • 0034139059 scopus 로고    scopus 로고
    • Mathematical programs with complementarity constraints: Stationarity, optimality and sensitivity
    • pp
    • H. SCHEEL AND S. SCHOLTES, Mathematical programs with complementarity constraints: Stationarity, optimality and sensitivity, Mathematics of Operations Research, 25 (2000), pp. 1–22.
    • (2000) Mathematics of Operations Research , vol.25 , pp. 1-22
    • Scheel, H.1    Scholtes, S.2
  • 275
    • 0001347358 scopus 로고
    • Modified Cholesky factorizations for sparse preconditioners
    • ), pp
    • T. SCHLICK, Modified Cholesky factorizations for sparse preconditioners, SIAM Journal on Scientific Computing, 14 (1993), pp. 424–445.
    • (1993) SIAM Journal on Scientific Computing , vol.14 , pp. 424-445
    • Schlick, T.1
  • 278
    • 0039515981 scopus 로고
    • On the order of convergence of certain quasi-Newton methods
    • ), pp
    • G. SCHULLER, On the order of convergence of certain quasi-Newton methods, Numerische Mathematik, 23 (1974), pp. 181–192.
    • (1974) Numerische Mathematik , vol.23 , pp. 181-192
    • Schuller, G.1
  • 279
    • 0022015590 scopus 로고
    • A family of trust-region-based algorithms for unconstrained minimization with strong global convergence properties
    • ), pp
    • G. A. SCHULTZ, R. B. SCHNABEL, AND R. H. BYRD, A family of trust-region-based algorithms for unconstrained minimization with strong global convergence properties, SIAM Journal on Numerical Analysis, 22 (1985), pp. 47–67.
    • (1985) SIAM Journal on Numerical Analysis , vol.22 , pp. 47-67
    • Schultz, G.A.1    Schnabel, R.B.2    Byrd, R.H.3
  • 280
    • 0004246963 scopus 로고
    • John Wiley & Sons, New York
    • G. A. F. SEBER AND C. J. WILD, Nonlinear Regression, John Wiley & Sons, New York, 1989.
    • (1989) Nonlinear Regression
  • 281
    • 0000305846 scopus 로고
    • The conjugate gradient method and trust regions in large scale optimization
    • ), pp
    • T. STEIHAUG, The conjugate gradient method and trust regions in large scale optimization, SIAM Journal on Numerical Analysis, 20 (1983), pp. 626–637.
    • (1983) SIAM Journal on Numerical Analysis , vol.20 , pp. 626-637
    • Steihaug, T.1
  • 282
    • 1842721333 scopus 로고
    • On the relation between quadratic termination and convergence properties of minimization algorithms. Part I: Theory
    • ), pp
    • J. STOER, On the relation between quadratic termination and convergence properties of minimization algorithms. Part I: Theory, Numerische Mathematik, 28 (1977), pp. 343–366.
    • (1977) Numerische Mathematik , vol.28 , pp. 343-366
    • Stoer, J.1
  • 283
    • 85098053359 scopus 로고    scopus 로고
    • K. TANABE, Centered Newton method for mathematical programming, in System Modeling and Optimization: Proceedings of the 13th IFIP conference, vol. 113 of Lecture Notes in Control and Information Systems, Berlin, 1988, Springer-Verlag, pp. 197–206
    • K. TANABE, Centered Newton method for mathematical programming, in System Modeling and Optimization: Proceedings of the 13th IFIP conference, vol. 113 of Lecture Notes in Control and Information Systems, Berlin, 1988, Springer-Verlag, pp. 197–206.
  • 284
    • 0002149307 scopus 로고    scopus 로고
    • Potential reduction methods in mathematical programming
    • ), pp
    • M. J. TODD, Potential reduction methods in mathematical programming, Mathematical Programming, Series B, 76 (1997), pp. 3–45.
    • (1997) Mathematical Programming, Series B , vol.76 , pp. 3-45
    • Todd, M.J.1
  • 285
    • 0000920501 scopus 로고    scopus 로고
    • Semidefinite optimization
    • ), pp
    • , Semidefinite optimization, Acta Numerica, 10 (2001), pp. 515–560.
    • (2001) Acta Numerica , vol.10 , pp. 515-560
  • 286
    • 85098066323 scopus 로고    scopus 로고
    • Detecting infeasibility in infeasible-interior-point methods for optimization, in Foundations of Computational Mathematics, Minneapolis, 2002, F. Cucker, R. DeVore, P. Olver, and E. Suli, eds., Cambridge University Press, Cambridge, 2004, pp. 157–192
    • , Detecting infeasibility in infeasible-interior-point methods for optimization, in Foundations of Computational Mathematics, Minneapolis, 2002, F. Cucker, R. DeVore, P. Olver, and E. Suli, eds., Cambridge University Press, Cambridge, 2004, pp. 157–192.
  • 287
    • 0012595684 scopus 로고
    • A centered projective algorithm for linear programming
    • ), pp
    • M. J. TODD AND Y. YE, A centered projective algorithm for linear programming, Mathematics of Operations Research, 15 (1990), pp. 508–529.
    • (1990) Mathematics of Operations Research , vol.15 , pp. 508-529
    • Todd, M.J.1    Ye, Y.2
  • 288
    • 0007113630 scopus 로고
    • On sparse and symmetric matrix updating subject to a linear equation
    • ), pp
    • P. L. TOINT, On sparse and symmetric matrix updating subject to a linear equation, Mathematics of Computation, 31 (1977), pp. 954–961.
    • (1977) Mathematics of Computation , vol.31 , pp. 954-961
    • Toint, P.L.1
  • 289
    • 0002633896 scopus 로고
    • Towards an efficient sparsity exploiting Newton method for minimization
    • Academic Press, New York, pp
    • , Towards an efficient sparsity exploiting Newton method for minimization, in Sparse Matrices and Their Uses, Academic Press, New York, 1981, pp. 57–87.
    • (1981) Sparse Matrices and Their Uses , pp. 57-87
  • 291
    • 14944387007 scopus 로고    scopus 로고
    • A globally convergence primal-dual interior-point filter method for nonlinear programming
    • ), pp
    • M. ULBRICH, S. ULBRICH, AND L. N. VICENTE, A globally convergence primal-dual interior-point filter method for nonlinear programming, Mathematical Programming, Series B, 100 (2004), pp. 379–410.
    • (2004) Mathematical Programming, Series B , vol.100 , pp. 379-410
    • Ulbrich, M.1    Ulbrich, S.2    Vicente, L.N.3
  • 292
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • ), pp
    • L. VANDENBERGHE AND S. BOYD, Semidefinite programming, SIAM Review, 38 (1996), pp. 49–95.
    • (1996) SIAM Review , vol.38 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2
  • 294
    • 0000287204 scopus 로고    scopus 로고
    • ] R. J. VANDERBEI AND D. F. SHANNO, An interior point algorithm for nonconvex nonlinear programming, ), pp
    • ] R. J. VANDERBEI AND D. F. SHANNO, An interior point algorithm for nonconvex nonlinear programming, Computational Optimization and Applications, 13 (1999), pp. 231–252.
    • (1999) Computational Optimization and Applications , vol.13 , pp. 231-252
  • 295
    • 0022076594 scopus 로고
    • A trust region algorithm for equality constrained minimization: Convergence properties and implementation
    • ), pp
    • A. VARDI, A trust region algorithm for equality constrained minimization: convergence properties and implementation, SIAM Journal of Numerical Analysis, 22 (1985), pp. 575–591.
    • (1985) SIAM Journal of Numerical Analysis , vol.22 , pp. 575-591
    • Vardi, A.1
  • 296
  • 297
    • 0005661496 scopus 로고
    • Oxford University Press, New York and Oxford
    • , Nonlinear Optimization, Oxford University Press, New York and Oxford, 1991.
    • (1991) Nonlinear Optimization
  • 299
    • 0000892372 scopus 로고    scopus 로고
    • Failure of global convergence for a class of interior point methods for nonlinear programming
    • ), pp
    • A. WÄCHTER AND L. T. BIEGLER, Failure of global convergence for a class of interior point methods for nonlinear programming, Mathematical Programming, 88 (2000), pp. 565–574.
    • (2000) Mathematical Programming , vol.88 , pp. 565-574
    • Wächter, A.1    Biegler, L.T.2
  • 300
    • 33144460598 scopus 로고    scopus 로고
    • Line search filter methods for nonlinear programming: Motivation and global convergence
    • ), pp
    • , Line search filter methods for nonlinear programming: Motivation and global convergence, SIAM Journal on Optimization, 16 (2005), pp. 1–31.
    • (2005) SIAM Journal on Optimization , vol.16 , pp. 1-31
  • 301
    • 29144523061 scopus 로고    scopus 로고
    • On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
    • ), pp
    • , On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Mathematical Programming, 106 (2006), pp. 25–57.
    • (2006) Mathematical Programming , vol.106 , pp. 25-57
  • 302
    • 0000043097 scopus 로고
    • Implementation of the GMRES method using Householder transformations
    • ), pp
    • H. WALKER, Implementation of the GMRES method using Householder transformations, SIAM Journal on Scientific and Statistical Computing, 9 (1989), pp. 815–825.
    • (1989) SIAM Journal on Scientific and Statistical Computing , vol.9 , pp. 815-825
    • Walker, H.1
  • 303
    • 85033419555 scopus 로고    scopus 로고
    • Evanston, IL, USA, June
    • R. A. WALTZ, J. L. MORALES, J. NOCEDAL, AND D. ORBAN, An interior algorithm for nonlinear optimization that combines line search and trust region steps, Tech. Rep. 2003-6, Optimization Technology Center, Northwestern University, Evanston, IL, USA, June 2003.
    • (2003) Northwestern University
  • 304
    • 85098092742 scopus 로고
    • INC, Maple V software package
    • WATERLOO MAPLE SOFTWARE, INC, Maple V software package, 1994.
    • (1994) MAPLE SOFTWARE
  • 305
    • 0022900476 scopus 로고
    • Numerical linear algebra aspects of globally convergent homotopy methods
    • ), pp
    • L. T. WATSON, Numerical linear algebra aspects of globally convergent homotopy methods, SIAM Review, 28 (1986), pp. 529–545.
    • (1986) SIAM Review , vol.28 , pp. 529-545
    • Watson, L.T.1
  • 308
    • 85098065322 scopus 로고    scopus 로고
    • Operations Research, Wadsworth Publishing Co., third ed
    • W. L. WINSTON, Operations Research, Wadsworth Publishing Co., third ed., 1997.
    • (1997)
    • Winston, W.L.1
  • 309
    • 0000557604 scopus 로고
    • A duality theorem for nonlinear programming
    • ), pp
    • P. WOLFE, A duality theorem for nonlinear programming, Quarterly of Applied Mathematics, 19 (1961), pp. 239–244.
    • (1961) Quarterly of Applied Mathematics , vol.19 , pp. 239-244
    • Wolfe, P.1
  • 310
    • 0002839203 scopus 로고
    • The composite simplex algorithm
    • ), pp
    • , The composite simplex algorithm, SIAM Review, 7 (1965), pp. 42–54.
    • (1965) SIAM Review , vol.7 , pp. 42-54
  • 311
    • 0004149831 scopus 로고    scopus 로고
    • Cambridge University Press and Wolfram Media, Inc., third ed
    • S. WOLFRAM, The Mathematica Book, Cambridge University Press and Wolfram Media, Inc., third ed., 1996.
    • (1996) The Mathematica Book
    • Wolfram, S.1
  • 315
    • 0003235254 scopus 로고    scopus 로고
    • Applying new optimization algorithms to model predictive control
    • Kantor, ed., CACHE
    • S. J. WRIGHT, Applying new optimization algorithms to model predictive control, in Chemical Process Control-V, J. C. Kantor, ed., CACHE, 1997.
    • Chemical Process Control-V, J. C , pp. 1997
    • Wright, S.J.1
  • 316
    • 85098085119 scopus 로고    scopus 로고
    • Primal-Dual Interior-Point Methods, SIAM Publications, Philadelphia, PA
    • , Primal-Dual Interior-Point Methods, SIAM Publications, Philadelphia, PA, 1997.
    • (1997)
  • 317
    • 0033432390 scopus 로고    scopus 로고
    • Modified Cholesky factorizations in interior-point algorithms for linear programming
    • ), pp
    • , Modified Cholesky factorizations in interior-point algorithms for linear programming, SIAM Journal on Optimization, 9 (1999), pp. 1159–1191.
    • (1999) SIAM Journal on Optimization , vol.9 , pp. 1159-1191
  • 319
    • 0036354771 scopus 로고    scopus 로고
    • Warm-start strategies in interior-point methods for linear programming
    • ), pp
    • E. A. YILDIRIM AND S. J. WRIGHT, Warm-start strategies in interior-point methods for linear programming, SIAM Journal on Optimization, 12 (2002), pp. 782–810.
    • (2002) SIAM Journal on Optimization , vol.12 , pp. 782-810
    • Yildirim, E.A.1    Wright, S.J.2
  • 320
    • 0347433923 scopus 로고    scopus 로고
    • On the truncated conjugate-gradient method
    • ), pp
    • Y. YUAN, On the truncated conjugate-gradient method, Mathematical Programming, Series A, 87 (2000), pp. 561–573.
    • (2000) Mathematical Programming, Series A , vol.87 , pp. 561-573
    • Yuan, Y.1
  • 321
    • 0032303559 scopus 로고    scopus 로고
    • Solving large-scale linear programs with interior-point methods under the Matlab environment
    • ), pp
    • Y. ZHANG, Solving large-scale linear programs with interior-point methods under the Matlab environment, Optimization Methods and Software, 10 (1998), pp. 1–31.
    • (1998) Optimization Methods and Software , vol.10 , pp. 1-31
    • Zhang, Y.1
  • 322
    • 0031345518 scopus 로고    scopus 로고
    • Algorithm 778: L-BFGS-B, FORTRAN subroutines for large scale bound constrained optimization
    • ), pp
    • C. ZHU, R. H. BYRD, P. LU, AND J. NOCEDAL, Algorithm 778: L-BFGS-B, FORTRAN subroutines for large scale bound constrained optimization, ACM Transactions on Mathematical Software, 23 (1997), pp. 550–560.
    • (1997) ACM Transactions on Mathematical Software , vol.23 , pp. 550-560
    • Zhu, C.1    Byrd, R.H.2    Lu, P.3    Nocedal, J.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.