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Volumn 28, Issue 4, 2013, Pages 871-888

A trust region method based on a new affine scaling technique for simple bounded optimization

Author keywords

affine scaling; bound constrained optimization; interior point; trust region

Indexed keywords

AFFINE SCALING; AFFINE SCALING METHOD; BOUND CONSTRAINED OPTIMIZATION; INTERIOR POINT; MATLAB OPTIMIZATION TOOLBOX; NUMERICAL PERFORMANCE; QUADRATIC APPROXIMATION; TRUST REGION;

EID: 84880247784     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556788.2011.622378     Document Type: Conference Paper
Times cited : (16)

References (37)
  • 1
    • 0022808141 scopus 로고
    • A variation on karmarkar's algorithm for solving linear programming problems
    • E.R. Barnes, A variation on Karmarkar's algorithm for solving linear programming problems, Math. Program. 36 (1986), pp. 174-182.
    • (1986) Math. Program. , vol.36 , pp. 174-182
    • Barnes, E.R.1
  • 2
    • 0037298205 scopus 로고    scopus 로고
    • An affine scaling trust-region approach to bound-constrained nonlinear systems
    • S. Bellavia, M. Macconi, and B. Morini, An affine scaling trust-region approach to bound-constrained nonlinear systems Appl. Numer. Math. 44 (2003), PP. 257-280.
    • (2003) Appl. Numer. Math. , vol.44 , pp. 257-280
    • Bellavia, S.1    Macconi, M.2    Morini, B.3
  • 3
    • 0036794059 scopus 로고    scopus 로고
    • Large-scale active-set box-constrained optimization method with spectral projected gradients
    • E.G. Birgin and J.M. Martinez, Large-scale active-set box-constrained optimization method with spectral projected gradients, Comput. Optim. Appl. 23 (2002), pp. 101-125.
    • (2002) Comput. Optim. Appl. , vol.23 , pp. 101-125
    • Birgin, E.G.1    Martinez, J.M.2
  • 4
    • 0010766006 scopus 로고
    • The trust region affine interior point algorithm for convex and nonconvex quadratic programming
    • J. Bonnans and M. Bouhtou, The trust region affine interior point algorithm for convex and nonconvex quadratic programming, RAIRO Rech. Opér. 29 (1995), pp. 195-217.
    • (1995) RAIRO Rech. Opér. , vol.29 , pp. 195-217
    • Bonnans, J.1    Bouhtou, M.2
  • 5
    • 0000732463 scopus 로고
    • A limited memory algorithm for bound constrained optimization
    • R.H. Byrd, P. Lu, J. Nocedal, and C. Zhu, A limited memory algorithm for bound constrained optimization, SIAM J. Sci. Comput. 16 (1995), pp. 1190-1208.
    • (1995) SIAM J. Sci. Comput. , vol.16 , pp. 1190-1208
    • Byrd, R.H.1    Lu, P.2    Nocedal, J.3    Zhu, C.4
  • 6
    • 43949154166 scopus 로고
    • On the convergence of interior-reflection Newton methods for nonlinear minimization subject to bounds
    • T.F. Coleman andY. Li, On the convergence of interior-reflection Newton methods for nonlinear minimization subject to bounds, Math. Program. 67 (1994), pp. 189-224.
    • (1994) Math. Program. , vol.67 , pp. 189-224
    • Coleman, T.F.1    Li, Y.2
  • 7
    • 0030303844 scopus 로고    scopus 로고
    • An interior trust region approach for nonlinear minimization subject to bounds
    • T.F. Coleman and Y. Li, An interior trust region approach for nonlinear minimization subject to bounds, SIAM J. Optim. 6 (1996), pp. 418-445.
    • (1996) SIAM J. Optim. , vol.6 , pp. 418-445
    • Coleman, T.F.1    Li, Y.2
  • 8
    • 0002467356 scopus 로고
    • Global convergence of a class of trust region algorithms for optimization with simple bounds
    • 26 (1989), 764-767
    • A.R. Conn, N.I.M. Gould, and Ph.L. Toint, Global convergence of a class of trust region algorithms for optimization with simple bounds, SIAM J. Numer. Anal. 25 (1988), pp. 433-460; 26 (1989), pp. 764-767.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 433-460
    • Conn, A.R.1    Gould, N.I.M.2    Toint, Ph.L.3
  • 11
    • 15544385032 scopus 로고    scopus 로고
    • Projected barzilai-borwein methods for large-scale box-constrained quadratic programming
    • Y.H. Dai and R. Fletcher, Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming, Numer. Math. 100 (2005), pp. 21-47.
    • (2005) Numer. Math. , vol.100 , pp. 21-47
    • Dai, Y.H.1    Fletcher, R.2
  • 12
    • 0012448399 scopus 로고    scopus 로고
    • Trust-region interior-point algorithms for minimization problems with simple bounds
    • K. Ritter, H. Fisher, H. Riedmüller and S. Schäffler, eds., Physica-Verlag, Springer, Berlin
    • J.E. Dennis and L.N.Vicente, Trust-region interior-point algorithms for minimization problems with simple bounds, in Applied Mathematics and Paralle Computing, K. Ritter, H. Fisher, H. Riedmüller and S. Schäffler, eds., Physica- Verlag, Springer, Berlin, 1996, pp. 97-107.
    • (1996) Applied Mathematics and Paralle Computing , pp. 97-107
    • Dennis, J.E.1    Vicente, L.N.2
  • 13
    • 0001031964 scopus 로고
    • Iterative solution of problems of linear and quadratic programming
    • Transl. Soviet Math. Dokl. 8 (1967), pp. 674-675.
    • I.I. Dikin, Iterative solution of problems of linear and quadratic programming, Dokl. Akad. Nauk SSSR 174 (1967), pp. 747-748. (Transl. Soviet Math. Dokl. 8 (1967), pp. 674-675.)
    • (1967) Dokl. Akad. Nauk SSSR , vol.174 , pp. 747-748
    • Dikin, I.I.1
  • 15
    • 28244496090 scopus 로고    scopus 로고
    • Benchmarking optimization software with performance profiles
    • E.D. Dolan and J.J. Moré, Benchmarking optimization software with performance profiles, Math. Program. 91 (2002), pp. 201-213.
    • (2002) Math. Program. , vol.91 , pp. 201-213
    • Dolan, E.D.1    Moré, J.J.2
  • 16
    • 0038342659 scopus 로고    scopus 로고
    • An active set Newton's algorithm for large-scale nonlinear programs with box constraints
    • F. Facchinei, J. Júdice, and J. Soares, An active set Newton's algorithm for large-scale nonlinear programs with box constraints, SIAM J. Optim. 8 (1998), pp. 158-186.
    • (1998) SIAM J. Optim. , vol.8 , pp. 158-186
    • Facchinei, F.1    Júdice, J.2    Soares, J.3
  • 17
    • 0036433456 scopus 로고    scopus 로고
    • A truncated Newton algorithm for large scale box constrained optimization
    • F. Facchinei, S. Lucidi, and L. Palagi, A truncated Newton algorithm for large scale box constrained optimization, SIAM J. Optim. 12 (2002), pp. 1100-1125.
    • (2002) SIAM J. Optim. , vol.12 , pp. 1100-1125
    • Facchinei, F.1    Lucidi, S.2    Palagi, L.3
  • 18
    • 0028532624 scopus 로고
    • A new trust region algorithm for bound constrained minimization
    • A. Friedlander, J.M. Martinez, and S. Santos, A new trust region algorithm for bound constrained minimization, Appl. Math. Optim. 30 (1994), pp. 235-266.
    • (1994) Appl. Math. Optim. , vol.30 , pp. 235-266
    • Friedlander, A.1    Martinez, J.M.2    Santos, S.3
  • 19
    • 2442598318 scopus 로고    scopus 로고
    • CUTEr, a constrained and unconstrained testing environment (revisited)
    • N.I.M. Gould, D. Orban, and Ph.L. Toint, CUTEr, a constrained and unconstrained testing environment (revisited), ACM Trans. Math. Softw. 29 (2003), pp. 373-394.
    • (2003) ACM Trans. Math. Softw. , vol.29 , pp. 373-394
    • Gould, N.I.M.1    Orban, D.2    Toint, Ph.L.3
  • 20
    • 55849087653 scopus 로고    scopus 로고
    • A recursive l∞-trust-region method for boundconstrained nonlinear optimization
    • S. Gratton, M. Mouffe, Ph.L. Toint, and M. Weber-Mendonça, A recursive l∞-trust-region method for boundconstrained nonlinear optimization, IMA. J. Numer. Anal. 28 (2008), pp. 827-861.
    • (2008) IMA. J. Numer. Anal. , vol.28 , pp. 827-861
    • Gratton, S.1    Mouffe, M.2    Toint, Ph.L.3    Weber-Mendonça, M.4
  • 21
    • 34249008073 scopus 로고    scopus 로고
    • A new active set algorithm for box constrained optimization
    • W.W. Hager and H.C. Zhang, A new active set algorithm for box constrained optimization, SIAM J. Optim. 17 (2006), pp. 526-557.
    • (2006) SIAM J. Optim. , vol.17 , pp. 526-557
    • Hager, W.W.1    Zhang, H.C.2
  • 22
    • 0000860416 scopus 로고    scopus 로고
    • Superlinear and quadratic convergence of affine-scaling interiorpoint Newton methods for problems with simple bounds without strict complementarity assumption
    • M. Heinkenschloss, M. Ulbrich, and S. Ulbrich, Superlinear and quadratic convergence of affine-scaling interiorpoint Newton methods for problems with simple bounds without strict complementarity assumption, Math. Program. 86 (1999), pp. 615-635.
    • (1999) Math. Program. , vol.86 , pp. 615-635
    • Heinkenschloss, M.1    Ulbrich, M.2    Ulbrich, S.3
  • 23
    • 33749615719 scopus 로고    scopus 로고
    • On affine scaling interior-point Newton methods for nonlinear minimization with bound constraints
    • C. Kanzow and A. Klug, On affine scaling interior-point Newton methods for nonlinear minimization with bound constraints, Comput. Optim. Appl. 35 (2006), pp. 177-197.
    • (2006) Comput. Optim. Appl. , vol.35 , pp. 177-197
    • Kanzow, C.1    Klug, A.2
  • 24
    • 0026136905 scopus 로고
    • Convergence of trust region algorithms for optimization with bounds when strict complementarity does not hold
    • M. Lescrenier, Convergence of trust region algorithms for optimization with bounds when strict complementarity does not hold, SIAM J. Numer. Anal. 28 (1991), pp. 476-495.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 476-495
    • Lescrenier, M.1
  • 25
    • 0033436056 scopus 로고    scopus 로고
    • Newton's method for large bound-constrained optimization problem
    • C. Lin and J.J. Moré, Newton's method for large bound-constrained optimization problem, SIAM J. Optim. 9 (1999), pp. 1100-1127.
    • (1999) SIAM J. Optim. , vol.9 , pp. 1100-1127
    • Lin, C.1    Moré, J.J.2
  • 26
    • 0032330782 scopus 로고    scopus 로고
    • Global convergence of the affine scaling algorithm for convex quadratic programmming
    • R.D.C. Monteiro and T. Tsuchiya, Global convergence of the affine scaling algorithm for convex quadratic programmming, SIAM J. Optim. 8 (1998), pp. 26-58.
    • (1998) SIAM J. Optim. , vol.8 , pp. 26-58
    • Monteiro, R.D.C.1    Tsuchiya, T.2
  • 27
    • 0012035936 scopus 로고    scopus 로고
    • Trust region affine scaling algorithms for linearly constrained convex and concave programs
    • R.D.C. Monteiro and Y. Wang, Trust region affine scaling algorithms for linearly constrained convex and concave programs, Math. Program. 80 (1998), pp. 283-313.
    • (1998) Math. Program. , vol.80 , pp. 283-313
    • Monteiro, R.D.C.1    Wang, Y.2
  • 28
    • 33845418028 scopus 로고
    • On the solution of large quadratic programming problems with bound constraints
    • J.J. Moré and G. Toraldo, On the solution of large quadratic programming problems with bound constraints, SIAM J. Optim. 1 (1991), pp. 93-113.
    • (1991) SIAM J. Optim. , vol.1 , pp. 93-113
    • Moré, J.J.1    Toraldo, G.2
  • 29
    • 0031525729 scopus 로고    scopus 로고
    • A subspace limited memory quasi-Newton algorithm for large-scale nonlinear bound constrained optimization
    • Q. Ni and Y.Yuan, A subspace limited memory quasi-Newton algorithm for large-scale nonlinear bound constrained optimization, Math. Comput. 66 (1997), pp. 1509-1520.
    • (1997) Math. Comput. , vol.66 , pp. 1509-1520
    • Ni, Q.1    Yuan, Y.2
  • 30
    • 77952487199 scopus 로고    scopus 로고
    • The BOBYQA algorithm for bound constrained optimization without derivatives
    • Department of Applied Mathematics and Theoretical Physics, NA2009/06, Cambridge
    • M.J.D. Powell, The BOBYQA algorithm for bound constrained optimization without derivatives, Technical Report, Department of Applied Mathematics and Theoretical Physics, NA2009/06, Cambridge, 2009.
    • (2009) Technical Report
    • Powell, M.J.D.1
  • 31
    • 0031542781 scopus 로고    scopus 로고
    • Family of projected descent methods for optimization problems with simple bounds
    • A. Schwartz and E. Polak, Family of projected descent methods for optimization problems with simple bounds, J. Optim. Theory Appl. 92 (1997), pp. 1-31.
    • (1997) J. Optim. Theory Appl. , vol.92 , pp. 1-31
    • Schwartz, A.1    Polak, E.2
  • 32
    • 21344451083 scopus 로고    scopus 로고
    • A convergence analysis for a convex version of Dikin's algorithm
    • J. Sun, A convergence analysis for a convex version of Dikin's algorithm, Ann. Oper. Res. 62 (1996), pp. 357-374.
    • (1996) Ann. Oper. Res. , vol.62 , pp. 357-374
    • Sun, J.1
  • 33
    • 14644406787 scopus 로고    scopus 로고
    • Convergence properties of Dikin's affine scaling algorithm for nonconvex quadratic minimization
    • P. Tseng, Convergence properties of Dikin's affine scaling algorithm for nonconvex quadratic minimization, J. Glob. Optim. 30 (2004), pp. 285-300.
    • (2004) J. Glob. Optim. , vol.30 , pp. 285-300
    • Tseng, P.1
  • 34
    • 0032651455 scopus 로고    scopus 로고
    • Global convergence of trust-region interior-point algorithms for infinite-dimensional nonconvex minimization subject to point-wise bounds
    • M. Ulbrich, S. Ulbrich, and M. Heinkenschloss, Global convergence of trust-region interior-point algorithms for infinite-dimensional nonconvex minimization subject to point-wise bounds, SIAM J. Control Optim. 37 (1999), pp. 731-764.
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 731-764
    • Ulbrich, M.1    Ulbrich, S.2    Heinkenschloss, M.3
  • 35
    • 33746951751 scopus 로고
    • A modification of Karmarkar's linear programming algorithm
    • R.J. Vanderbei, M.S. Meketon, and B.A. Freedman, A modification of Karmarkar's linear programming algorithm, Algorithmica 1 (1986), pp. 395-407.
    • (1986) Algorithmica , vol.1 , pp. 395-407
    • Vanderbei, R.J.1    Meketon, M.S.2    Freedman, B.A.3
  • 37
    • 0031345518 scopus 로고    scopus 로고
    • L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization
    • C. Zhu, R.H. Byrd, P. Lu, and J. Nocedal, L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization, ACM Trans. Math. Softw. 23 (1997), pp. 550-560.
    • (1997) ACM Trans. Math. Softw. , vol.23 , pp. 550-560
    • Zhu, C.1    Byrd, R.H.2    Lu, P.3    Nocedal, J.4


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