메뉴 건너뛰기




Volumn 152, Issue , 2005, Pages 1-213

Relaxation and decomposition methods for mixed integer nonlinear programming

(1)  Nowak, Ivo a  

a NONE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords


EID: 85093897261     PISSN: 03733149     EISSN: 22966072     Source Type: Book Series    
DOI: None     Document Type: Chapter
Times cited : (24)

References (219)
  • 2
    • 0032552250 scopus 로고    scopus 로고
    • A global optimization method, αBB, for general twice-differentiable constrained NLPs — I. Theoretical advances
    • Adjiman, C. S., Dallwig, S., Floudas, C. A., and Neumaier, A. (1998). A global optimization method, αBB, for general twice-differentiable constrained NLPs — I. Theoretical advances. Comp. Chem. Eng., pages 1137–1158.
    • (1998) Comp. Chem. Eng , pp. 1137-1158
    • Adjiman, C. S.1    Dallwig, S.2    Floudas, C. A.3    Neumaier, A.4
  • 3
    • 0003086747 scopus 로고    scopus 로고
    • Rigorous convex underestimators for general twice-differentiable problems
    • Adjiman, C. S. and Floudas, C. A. (1997). Rigorous convex underestimators for general twice-differentiable problems. J. Global Opt., 9:23–40.
    • (1997) J. Global Opt , vol.9 , pp. 23-40
    • Adjiman, C. S.1    Floudas, C. A.2
  • 7
    • 0000483159 scopus 로고
    • A relaxation method for nonconvex quadratically constrained quadratic programs
    • Al-Khayyal, F. A., Larsen, C., and van Voorhis, T. (1995). A relaxation method for nonconvex quadratically constrained quadratic programs. J. Glob. Opt, 6:215–230.
    • (1995) J. Glob. Opt , vol.6 , pp. 215-230
    • Al-Khayyal, F. A.1    Larsen, C.2    van Voorhis, T.3
  • 8
    • 1842734806 scopus 로고    scopus 로고
    • Accelerating convergence of branch-and-bound algorithms for quadratically constrained optimization problems
    • Floudas, C. A., editor, Kluwer Academic Publishers, Dordrecht
    • Al-Khayyal, F. A. and van Voorhis, T. (1996). Accelerating convergence of branch-and-bound algorithms for quadratically constrained optimization problems. In Floudas, C. A., editor, State of the Art in Global Optimization: Computational Methods and Applications. Kluwer Academic Publishers, Dordrecht.
    • (1996) State of the Art in Global Optimization: Computational Methods and Applications
    • Al-Khayyal, F. A.1    van Voorhis, T.2
  • 10
    • 0345808244 scopus 로고    scopus 로고
    • On Lagrangian relaxation of quadratic matrix constraints
    • Research Report CORR 98-24, Department of Combina-torics and Optimization,University of Waterloo
    • Anstreicher, K. and Wolkowicz, H. (1998). On Lagrangian relaxation of quadratic matrix constraints. Research Report CORR 98-24, Department of Combina-torics and Optimization,University of Waterloo.
    • (1998)
    • Anstreicher, K.1    Wolkowicz, H.2
  • 13
    • 0034551040 scopus 로고    scopus 로고
    • Global optimality conditions for quadratic optimization problems with binary constraints
    • Beck, A. and Teboulle, M. (2000). Global optimality conditions for quadratic optimization problems with binary constraints. SIAM J. Opt., pages 179– 188.
    • (2000) SIAM J. Opt , pp. 179-188
    • Beck, A.1    Teboulle, M.2
  • 15
    • 0039772219 scopus 로고    scopus 로고
    • Solving large-scale sparse semidefinite programs for combinatorial optimization
    • Benson, S. J., Ye, Y., and Zhang, X. (2000). Solving large-scale sparse semidefinite programs for combinatorial optimization. SIAM J. Optim., 10(2):443–461.
    • (2000) SIAM J. Optim , vol.10 , Issue.2 , pp. 443-461
    • Benson, S. J.1    Ye, Y.2    Zhang, X.3
  • 16
    • 0038809345 scopus 로고    scopus 로고
    • An approximation algorithm for the maximum cut problem and its experimental analysis
    • Berloni, A., Campadelli, P., and Grossi, G. (1998). An approximation algorithm for the maximum cut problem and its experimental analysis. Proceedings of “Algorithms and Experiments”, pages 137–143.
    • (1998) Proceedings of “Algorithms and Experiments , pp. 137-143
    • Berloni, A.1    Campadelli, P.2    Grossi, G.3
  • 18
    • 4043106821 scopus 로고    scopus 로고
    • Paragon Decision Technology B.V., Haarlem, The Netherlands
    • Bisschop, J. and Roelofs, M. (2002). AIMMS-The User’s Guide. Paragon Decision Technology B.V., Haarlem, The Netherlands, http://www.aimms.com.
    • (2002) AIMMS-The User’s Guide
    • Bisschop, J.1    Roelofs, M.2
  • 19
    • 84889982153 scopus 로고    scopus 로고
    • Solving Real-World Linear Programs: A Decade and More of Progress
    • To appear in Operations Research
    • Bixby, R. (2001). Solving Real-World Linear Programs: A Decade and More of Progress. To appear in Operations Research.
    • (2001)
    • Bixby, R.1
  • 22
    • 0242543462 scopus 로고    scopus 로고
    • A new method for the global solution of large systems of continuous constraints
    • Bliek, C., Jermann, C., and Neumaier, A., editors, pages Springer, Berlin
    • Boddy, M. and Johnson, D. (2003). A new method for the global solution of large systems of continuous constraints. In Bliek, C., Jermann, C., and Neumaier, A., editors, Global Optimization and Constraint Satisfaction, pages 142–156. Springer, Berlin.
    • (2003) Global Optimization and Constraint Satisfaction , pp. 142-156
    • Boddy, M.1    Johnson, D.2
  • 23
    • 0002017426 scopus 로고
    • Stochastic methods
    • Horst, R. and Pardalos, P., editors, pages Kluwer Academic Publishers, Dordrecht
    • Boender, C. G. E. and Romeijn, H. E. (1995). Stochastic methods. In Horst, R. and Pardalos, P., editors, Handbook of Global Optimization, pages 829–869. Kluwer Academic Publishers, Dordrecht.
    • (1995) Handbook of Global Optimization , pp. 829-869
    • Boender, C. G. E.1    Romeijn, H. E.2
  • 24
    • 0000462690 scopus 로고    scopus 로고
    • On standard quadratic optimization problems
    • Bomze, I. (1998). On standard quadratic optimization problems. J. Global Opt., 13:369–387.
    • (1998) J. Global Opt , vol.13 , pp. 369-387
    • Bomze, I.1
  • 27
    • 0036013024 scopus 로고    scopus 로고
    • Rank-two relaxation heuristics for max-cut and other binary quadratic programs
    • Burer, S., Monteiro, R. D. C., and Zhang, Y. (2001). Rank-two relaxation heuristics for max-cut and other binary quadratic programs. SIAM J.Opt., 12:503– 521.
    • (2001) SIAM J.Opt , vol.12 , pp. 503-521
    • Burer, S.1    Monteiro, R. D. C.2    Zhang, Y.3
  • 29
    • 3843076327 scopus 로고    scopus 로고
    • MINLPLib-A Collection of Test Models for Mixed-Integer Nonlinear Programming
    • Bussieck, M., Drud, A., and Meeraus, A. (2003a). MINLPLib-A Collection of Test Models for Mixed-Integer Nonlinear Programming. INFORMS J. Comput., 15(1).
    • (2003) INFORMS J. Comput , vol.15 , Issue.1
    • Bussieck, M.1    Drud, A.2    Meeraus, A.3
  • 37
    • 0001391104 scopus 로고
    • Decomposition principle for linear programs
    • Dantzig, G. B. and Wolfe, P. (1960). Decomposition principle for linear programs. Operations Research, 8:101–111.
    • (1960) Operations Research , vol.8 , pp. 101-111
    • Dantzig, G. B.1    Wolfe, P.2
  • 38
    • 0000039065 scopus 로고
    • The decomposition algorithm for linear programs
    • Dantzig, G. B. and Wolfe, P. (1961). The decomposition algorithm for linear programs. Econometrica, 29:767–778.
    • (1961) Econometrica , vol.29 , pp. 767-778
    • Dantzig, G. B.1    Wolfe, P.2
  • 39
    • 85093885276 scopus 로고    scopus 로고
    • Dash Optimization
    • Dash Optimization (2003). XPRESS. http://www.dashopt.com.
    • (2003) XPRESS
  • 40
    • 0001026422 scopus 로고
    • Linear control of a Markov production system
    • Demands, E. V. and Tang, C. S. (1992). Linear control of a Markov production system. Operations Research, 40:259–278.
    • (1992) Operations Research , vol.40 , pp. 259-278
    • Demands, E. V.1    Tang, C. S.2
  • 41
    • 26644456198 scopus 로고
    • Pathfollowing methods in nonlinear optimization III: multiplier embedding
    • Dentcheva, D., Guddat, J., and Rückmann, J.-J. (1995). Pathfollowing methods in nonlinear optimization III: multiplier embedding. ZOR-Math. Methods of OR, 41:127–152.
    • (1995) ZOR-Math. Methods of OR , vol.41 , pp. 127-152
    • Dentcheva, D.1    Guddat, J.2    Rückmann, J.-J.3
  • 42
    • 53849105217 scopus 로고    scopus 로고
    • Technical report, Preprint 02-5, Institut für Mathematik, Humboldt-Universität zu Berlin, accepted for publication in Math. Progr
    • Dentcheva, D. and Römisch, W. (2002). Duality gaps in nonconvex stochastic optimization. Technical report, Preprint 02-5, Institut für Mathematik, Humboldt-Universität zu Berlin, accepted for publication in Math. Progr.
    • (2002) Duality gaps in nonconvex stochastic optimization
    • Dentcheva, D.1    Römisch, W.2
  • 44
    • 84967782959 scopus 로고
    • On the numerical solution of heat conduction problems in two and three space variables
    • Douglas, J. and Rachford, H. (1956). On the numerical solution of heat conduction problems in two and three space variables. Trans. Amer. Math. Soc., 82:421– 439.
    • (1956) Trans. Amer. Math. Soc , vol.82 , pp. 421-439
    • Douglas, J.1    Rachford, H.2
  • 46
    • 33751071102 scopus 로고    scopus 로고
    • Scenario reduction in stochastic programming: An approach using probability metrics
    • to appear in
    • Dupacová, J., Gröwe-Kuska, N., and Römisch, W. (2003). Scenario reduction in stochastic programming: An approach using probability metrics. to appear in Math. Progr.
    • (2003) Math. Progr.
    • Dupacová, J.1    Gröwe-Kuska, N.2    Römisch, W.3
  • 47
    • 19644372491 scopus 로고    scopus 로고
    • Dual bounding procedures lead to convergent Branch-and-Bound algorithms
    • Dür, M. (2001). Dual bounding procedures lead to convergent Branch-and-Bound algorithms. Math. Progr., 91:117–125.
    • (2001) Math. Progr , vol.91 , pp. 117-125
    • Dür, M.1
  • 48
    • 0022902024 scopus 로고
    • An outer approximation algorithm for a class of mixed-integer nonlinear programs
    • Duran, M. A. and Grossmann, I. E. (1986). An outer approximation algorithm for a class of mixed-integer nonlinear programs. Math. Progr., 36:307.
    • (1986) Math. Progr , vol.36 , pp. 307
    • Duran, M. A.1    Grossmann, I. E.2
  • 49
    • 34250409962 scopus 로고
    • A central cutting plane algorithm for the convex programming problem
    • Elzinga, J. and Moore, T. (1975). A central cutting plane algorithm for the convex programming problem. Math. Progr., 8:134–145.
    • (1975) Math. Progr , vol.8 , pp. 134-145
    • Elzinga, J.1    Moore, T.2
  • 51
    • 0000703172 scopus 로고
    • Generalized Lagrange Multiplier Method for Solving Problems of Optimal Allocation of Resources
    • Everett, H. (1963). Generalized Lagrange Multiplier Method for Solving Problems of Optimal Allocation of Resources. Operations Research, 11:399–417.
    • (1963) Operations Research , vol.11 , pp. 399-417
    • Everett, H.1
  • 52
    • 46149129389 scopus 로고
    • Triangular Bernstein-Bézier patches
    • Farin, G. (1986). Triangular Bernstein-Bézier patches. Computer Aided Geometric Design, 3:83–127.
    • (1986) Computer Aided Geometric Design , vol.3 , pp. 83-127
    • Farin, G.1
  • 53
    • 0034377204 scopus 로고    scopus 로고
    • Dual applications of proximal bundle methods including lagrangian relaxation of nonconvex problems
    • Feltenmark, S. and Kiwiel, K. C. (2000). Dual applications of proximal bundle methods including lagrangian relaxation of nonconvex problems. SIAM J. Optim., 10(3):697–721.
    • (2000) SIAM J. Optim , vol.10 , Issue.3 , pp. 697-721
    • Feltenmark, S.1    Kiwiel, K. C.2
  • 54
    • 0040531891 scopus 로고    scopus 로고
    • Partitioning mathematical programs for parallel solution
    • Ferris, M. C. and Horn, J. D. (1998). Partitioning mathematical programs for parallel solution. Math. Progr., 80:35–61.
    • (1998) Math. Progr , vol.80 , pp. 35-61
    • Ferris, M. C.1    Horn, J. D.2
  • 56
    • 0023331318 scopus 로고    scopus 로고
    • Bilinear programming and structured stochastic games
    • Filar, J. A. and Schultz, T. A. (1999). Bilinear programming and structured stochastic games. J. Opt. Theor. Appl., 53:85–104.
    • (1999) J. Opt. Theor. Appl , vol.53 , pp. 85-104
    • Filar, J. A.1    Schultz, T. A.2
  • 57
    • 0008683322 scopus 로고
    • Worst-case analysis of heuristic algorithms
    • Fisher, M. L. (1980). Worst-case analysis of heuristic algorithms. Management Science, 26(1):1–17.
    • (1980) Management Science , vol.26 , Issue.1 , pp. 1-17
    • Fisher, M. L.1
  • 59
    • 33947605053 scopus 로고
    • Solving Mixed Integer Nonlinear Programs by Outer Approximation
    • Fletcher, R. and Leyffer, S. (1994). Solving Mixed Integer Nonlinear Programs by Outer Approximation. Math. Progr., 66:327.
    • (1994) Math. Progr , vol.66 , pp. 327
    • Fletcher, R.1    Leyffer, S.2
  • 60
    • 85093895456 scopus 로고    scopus 로고
    • Fletcher, R. and Leyffer, S. (2002). MINLP. http://www.maths.dundee.ac.uk/~sleyffer/MINLP.html.
    • (2002) MINLP
    • Fletcher, R.1    Leyffer, S.2
  • 61
    • 34250076248 scopus 로고
    • Decomposition in general mathematical programming
    • Flippo, O. E. and Kan, A. H. G. R. (1993). Decomposition in general mathematical programming. Math. Progr., 60:361–382.
    • (1993) Math. Progr , vol.60 , pp. 361-382
    • Flippo, O. E.1    Kan, A. H. G. R.2
  • 66
    • 0027640931 scopus 로고
    • Genetic algorithms: principles of natural selection applied to computation
    • Forrest, S. (1993). Genetic algorithms: principles of natural selection applied to computation. Science, pages 872–878.
    • (1993) Science , pp. 872-878
    • Forrest, S.1
  • 68
    • 0024765056 scopus 로고
    • APROS: Algorithmic development methodology for discrete-continuous optimization problems
    • I. and
    • G. E. Paules, I. and Floudas, C. A. (1989). APROS: Algorithmic development methodology for discrete-continuous optimization problems. Oper. Res., 37(6):902.
    • (1989) Oper. Res , vol.37 , Issue.6 , pp. 902
    • Paules, G. E.1    Floudas, C. A.2
  • 69
    • 0004034517 scopus 로고    scopus 로고
    • GAMS GAMS Development Corporation, Washington DC
    • GAMS (2003). GAMS-The Solver Manuals. GAMS Development Corporation, Washington DC.
    • (2003) GAMS-The Solver Manuals
  • 72
    • 24944468021 scopus 로고    scopus 로고
    • An improved method for the computation of affine lower bound functions for polynomials
    • Floudas, C. and Pardalos, P., editors, pages Kluwer Academic Publishers, Dordrecht
    • Garloff, J. and Smith, A. (2003). An improved method for the computation of affine lower bound functions for polynomials. In Floudas, C. and Pardalos, P., editors, Frontiers in Global Optimization, pages 1–10. Kluwer Academic Publishers, Dordrecht.
    • (2003) Frontiers in Global Optimization , pp. 1-10
    • Garloff, J.1    Smith, A.2
  • 73
    • 0015419856 scopus 로고
    • General Benders decomposition
    • Geoffrion, A. M. (1972). General Benders decomposition. J. Opt. Theor. Appl., 10 (4):237–260.
    • (1972) J. Opt. Theor. Appl , vol.10 , Issue.4 , pp. 237-260
    • Geoffrion, A. M.1
  • 74
    • 0002554041 scopus 로고
    • Lagrangian Relaxation for Integer Programming
    • Geoffrion, A. M. (1974). Lagrangian Relaxation for Integer Programming. Math. Progr. Study, 2:82–114.
    • (1974) Math. Progr. Study , vol.2 , pp. 82-114
    • Geoffrion, A. M.1
  • 75
    • 0003579442 scopus 로고    scopus 로고
    • Technical report, University of California, San Diego, Mathematics Department Report NA 97-4
    • Gill, P. E., Murray, W., and Saunders, M. A. (1997). SNOPT 5.3 user’s guide. Technical report, University of California, San Diego, Mathematics Department Report NA 97-4.
    • (1997) SNOPT 5.3 user’s guide
    • Gill, P. E.1    Murray, W.2    Saunders, M. A.3
  • 76
    • 0004215426 scopus 로고    scopus 로고
    • Kluwer Academic Publishers, Boston
    • Glover, F. and Laguna, M. (1997). Tabu Search. Kluwer Academic Publishers, Boston.
    • (1997) Tabu Search
    • Glover, F.1    Laguna, M.2
  • 78
    • 84893574327 scopus 로고
    • Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
    • Goemans, M. X. and Williamson, D. P. (1995). Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming. J. ACM, 42:1115–1145.
    • (1995) J. ACM , vol.42 , pp. 1115-1145
    • Goemans, M. X.1    Williamson, D. P.2
  • 79
    • 0002396293 scopus 로고
    • On convergence rate of subgradient optimization methods
    • Goffin, J. L. (1977). On convergence rate of subgradient optimization methods. Math. Progr., 13:329–347.
    • (1977) Math. Progr , vol.13 , pp. 329-347
    • Goffin, J. L.1
  • 81
    • 77956948383 scopus 로고    scopus 로고
    • Grossmann, I. (2002). DICOPT. http://www.gams.com/solvers/dicopt/main.htm.
    • (2002) DICOPT
    • Grossmann, I.1
  • 84
    • 0003077343 scopus 로고    scopus 로고
    • Mixed-integer nonlinear programming: A survey of algorithms and applications
    • Conn, A., Biegler, L., Coleman, T., and Santosa, F., editors, Springer, New York
    • Grossmann, I. E. and Kravanja, Z. (1997). Mixed-integer nonlinear programming: A survey of algorithms and applications. In Conn, A., Biegler, L., Coleman, T., and Santosa, F., editors, Large-Scale Optimization with Applicationa, Part II:Optimal Design and Control. Springer, New York.
    • (1997) Large-Scale Optimization with Applicationa, Part II:Optimal Design and Control
    • Grossmann, I. E.1    Kravanja, Z.2
  • 85
    • 83455199110 scopus 로고    scopus 로고
    • Special Issue on Mixed-Integer Programming and it’s Application to Engineering, Part I
    • Kluwer Academic Publishers, Dordrecht
    • Grossmann, I. E. and Sahinidis, N. (2002a). Special Issue on Mixed-Integer Programming and it’s Application to Engineering, Part I. Optim. Eng., 3(4), Kluwer Academic Publishers, Dordrecht.
    • (2002) Optim. Eng , vol.3 , Issue.4
    • Grossmann, I. E.1    Sahinidis, N.2
  • 86
    • 83455199110 scopus 로고    scopus 로고
    • Special Issue on Mixed-Integer Programming and it’s Application to Engineering, Part II
    • Kluwer Academic Publishers, Dordrecht
    • Grossmann, I. E. and Sahinidis, N. (2002b). Special Issue on Mixed-Integer Programming and it’s Application to Engineering, Part II. Optim. Eng., 4(1), Kluwer Academic Publishers, Dordrecht.
    • (2002) Optim. Eng , vol.4 , Issue.1
    • Grossmann, I. E.1    Sahinidis, N.2
  • 88
    • 26644436996 scopus 로고    scopus 로고
    • On the role of the Mangasarian-Fromovitz constraints qualification for penalty-, exact penalty-and Lagrange multiplier methods
    • Fiacco, A. editor, pages Marcel Deckker, Inc., New York
    • Guddat, J., Guerra, F., and Nowack, D. (1998). On the role of the Mangasarian-Fromovitz constraints qualification for penalty-, exact penalty-and Lagrange multiplier methods. In Fiacco, A. V., editor, Mathematical Programming with Data Perturbations, pages 159–183. Marcel Deckker, Inc., New York.
    • (1998) Mathematical Programming with Data Perturbations , pp. 159-183
    • Guddat, J.1    Guerra, F.2    Nowack, D.3
  • 90
    • 0023451776 scopus 로고
    • Lagrangian decomposition: a model yielding stronger Lagrangean bounds
    • Guignard, M. and Kim, S. (1987). Lagrangian decomposition: a model yielding stronger Lagrangean bounds. Math. Progr., 39(2):215–228.
    • (1987) Math. Progr , vol.39 , Issue.2 , pp. 215-228
    • Guignard, M.1    Kim, S.2
  • 92
    • 1542307069 scopus 로고    scopus 로고
    • A spectral bundle method with bounds
    • Helmberg, C. and Kiwiel, K. C. (2002). A spectral bundle method with bounds. Math. Progr., 93(2):173–194.
    • (2002) Math. Progr , vol.93 , Issue.2 , pp. 173-194
    • Helmberg, C.1    Kiwiel, K. C.2
  • 93
    • 0034415006 scopus 로고    scopus 로고
    • A spectral bundle method for semidefinite programming
    • Helmberg, C. and Rendl, F. (2000). A spectral bundle method for semidefinite programming. SIAM J. Opt., 10(3):673–695.
    • (2000) SIAM J. Opt , vol.10 , Issue.3 , pp. 673-695
    • Helmberg, C.1    Rendl, F.2
  • 97
    • 0025444672 scopus 로고
    • On the convergence of the cross decomposition
    • Holmberg, K. (1990). On the convergence of the cross decomposition. Math. Progr., 47:269.
    • (1990) Math. Progr , vol.47 , pp. 269
    • Holmberg, K.1
  • 98
    • 0031076353 scopus 로고    scopus 로고
    • A lagrangian heuristic for the facility location problem with staircase costs
    • Holmberg, K. and Ling, J. (1997). A lagrangian heuristic for the facility location problem with staircase costs. Eur. J. Oper. Res., 97:63–74.
    • (1997) Eur. J. Oper. Res , vol.97 , pp. 63-74
    • Holmberg, K.1    Ling, J.2
  • 104
    • 85093879523 scopus 로고    scopus 로고
    • ILOG, Inc
    • ILOG, Inc. (2005). CPLEX. http://www.ilog.com/products/cplex/.
    • (2005) CPLEX
  • 108
    • 26444479778 scopus 로고
    • Optimization by simulated annealing
    • Kirkpatrick, S., Geddat Jr., C., and Vecchi, M. (1983). Optimization by simulated annealing. Science, 220:671–680.
    • (1983) Science , vol.220 , pp. 671-680
    • Kirkpatrick, S.1    Geddat, C.2    Vecchi, M.3
  • 109
    • 0025208765 scopus 로고
    • Proximity control in bundle methods for convex nondifferentiable minimization
    • Kiwiel, K. C. (1990). Proximity control in bundle methods for convex nondifferentiable minimization. Math. Progr., 46:105–122.
    • (1990) Math. Progr , vol.46 , pp. 105-122
    • Kiwiel, K. C.1
  • 111
    • 21844522404 scopus 로고
    • A cholesky dual method for proximal piecewise linear programming
    • Kiwiel, K. C. (1994a). A cholesky dual method for proximal piecewise linear programming. Numerische Mathematik, 68.
    • (1994) Numerische Mathematik , vol.68
    • Kiwiel, K. C.1
  • 112
    • 0023418970 scopus 로고
    • Relaxation strategy for the structural optimization of nonconvex MINLP problems in process flow sheets
    • Kocis, G. R. and Grossmann, I. E. (1987). Relaxation strategy for the structural optimization of nonconvex MINLP problems in process flow sheets. Ind. Eng. Chem. Res., 26(9):1869.
    • (1987) Ind. Eng. Chem. Res , vol.26 , Issue.9 , pp. 1869
    • Kocis, G. R.1    Grossmann, I. E.2
  • 113
    • 0242592654 scopus 로고    scopus 로고
    • A General Framework for Convex Relaxation of Polynomial Optimization Problems over Cones
    • Kojima, M., Kim, S., and Waki, H. (2003). A General Framework for Convex Relaxation of Polynomial Optimization Problems over Cones. Journal of Operations Research Society of Japan, 46(2):125–144.
    • (2003) Journal of Operations Research Society of Japan , vol.46 , Issue.2 , pp. 125-144
    • Kojima, M.1    Kim, S.2    Waki, H.3
  • 114
    • 85037295205 scopus 로고    scopus 로고
    • Moderate nonconvexity = convexity + quadratic concavity
    • Technical report, Research Reports on Mathematical and Comuting Sciences, Series B: Operations Research, Tokyo Institute of Technology, B-348
    • Kojima, M., Matsumoto, T., and Shida, M. (1999). Moderate nonconvexity = convexity + quadratic concavity. Technical report, Research Reports on Mathematical and Comuting Sciences, Series B: Operations Research, Tokyo Institute of Technology, B-348.
    • (1999)
    • Kojima, M.1    Matsumoto, T.2    Shida, M.3
  • 115
    • 0000446186 scopus 로고
    • Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken
    • Krawczyk, R. (1969). Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken. Computing, 4:187–2001.
    • (1969) Computing , vol.4 , pp. 187-2001
    • Krawczyk, R.1
  • 118
    • 85093901904 scopus 로고    scopus 로고
    • Lasdon (2003). OQNLP. http://www.gams.com/solvers/oqnlp.pdf.
    • (2003) OQNLP
    • Lasdon1
  • 119
    • 0035238864 scopus 로고    scopus 로고
    • Global optimization with polynomials and the problem of moments
    • Lasserre, J. B. (2001). Global optimization with polynomials and the problem of moments. SIAM J. Opt., 11(3):796–817.
    • (2001) SIAM J. Opt , vol.11 , Issue.3 , pp. 796-817
    • Lasserre, J. B.1
  • 120
    • 10844287617 scopus 로고    scopus 로고
    • Lagrangian relaxation
    • Lemaréchal, C. (2001). Lagrangian relaxation. Optimization Online. http://www.optimization-online.org/DB_HTML/2001/03/298.html.
    • (2001) Optimization Online
    • Lemaréchal, C.1
  • 122
    • 0344794572 scopus 로고    scopus 로고
    • A geometric study of duality gaps, with applications
    • Lemaréchal, C. and Renaud, A. (2001). A geometric study of duality gaps, with applications. Math. Progr., 90:399–427.
    • (2001) Math. Progr , vol.90 , pp. 399-427
    • Lemaréchal, C.1    Renaud, A.2
  • 124
    • 1642563297 scopus 로고    scopus 로고
    • Simulated annealing algorithms for continuous global optimization
    • Pardalos, P. and Romeijn, H., editors, pages Kluwer Academic Publishers, Dor-drecht
    • Locatelli, M. (2002). Simulated annealing algorithms for continuous global optimization. In Pardalos, P. and Romeijn, H., editors, Handbook of Global Optimization, Volume 2, pages 179–229. Kluwer Academic Publishers, Dor-drecht.
    • (2002) Handbook of Global Optimization , vol.2 , pp. 179-229
    • Locatelli, M.1
  • 126
    • 49949133603 scopus 로고
    • The Fritz John necessary optimality conditions in the presence of equality and inequality constraints
    • Mangasarin, O. L. and Fromowitz, S. (1967). The Fritz John necessary optimality conditions in the presence of equality and inequality constraints. J. Math. Anal. Appl., 17:37–37.
    • (1967) J. Math. Anal. Appl , vol.17 , pp. 37-37
    • Mangasarin, O. L.1    Fromowitz, S.2
  • 127
    • 0040905027 scopus 로고    scopus 로고
    • Technical report, ZIB Report 99–03, Habilitationsschrift
    • Martin, A. (1999). Integer programs with block structure. Technical report, ZIB– Report 99–03, Habilitationsschrift.
    • (1999) Integer programs with block structure
    • Martin, A.1
  • 128
    • 0347923972 scopus 로고
    • Solving nonlinear integer programs with large scale optimization software
    • Mawengkang, H. and Murtagh, B. (1986). Solving nonlinear integer programs with large scale optimization software. Ann. O. R., 5:425.
    • (1986) Ann. O. R , vol.5 , pp. 425
    • Mawengkang, H.1    Murtagh, B.2
  • 132
    • 0031285908 scopus 로고    scopus 로고
    • Global continuation for distance geometry problems
    • Moré, J. and Wu, Z. (1997). Global continuation for distance geometry problems. SIAM J. Optim., 7:814–836.
    • (1997) SIAM J. Optim , vol.7 , pp. 814-836
    • Moré, J.1    Wu, Z.2
  • 133
    • 0023452095 scopus 로고
    • Some NP-complete problems in quadratic and nonlinear programming
    • Murty, K. G. (1987). Some NP-complete problems in quadratic and nonlinear programming. Math. Progr., 39:117–129.
    • (1987) Math. Progr , vol.39 , pp. 117-129
    • Murty, K. G.1
  • 135
    • 85093890861 scopus 로고
    • NETLIB (-1973)
    • NETLIB (1972-1973). EISPACK. http://www.netlib.org/eispack/.
    • (1972) EISPACK
  • 137
    • 0344971507 scopus 로고
    • An optimality criterion for global quadratic optimization
    • Neumaier, A. (1992). An optimality criterion for global quadratic optimization. J. Global Opt., 2:201–208.
    • (1992) J. Global Opt , vol.2 , pp. 201-208
    • Neumaier, A.1
  • 138
    • 0001016206 scopus 로고    scopus 로고
    • Second-order sufficient optimality conditions for local and global nonlinear programming
    • Neumaier, A. (1996). Second-order sufficient optimality conditions for local and global nonlinear programming. J. Global Opt., 9:141–151.
    • (1996) J. Global Opt , vol.9 , pp. 141-151
    • Neumaier, A.1
  • 140
    • 2942655185 scopus 로고    scopus 로고
    • Complete search in continiuous global optimization and constraint satisfaction
    • Iserles, A., editor, pages Cambridge University Press, Cambridge, UK
    • Neumaier, A. (2004). Complete search in continiuous global optimization and constraint satisfaction. In Iserles, A., editor, Acta Numerica, pages 271–369. Cambridge University Press, Cambridge, UK.
    • (2004) Acta Numerica , pp. 271-369
    • Neumaier, A.1
  • 143
    • 0002376103 scopus 로고    scopus 로고
    • A new semidefinite programming bound for indefinite quadratic forms over a simplex
    • Nowak, I. (1999). A new semidefinite programming bound for indefinite quadratic forms over a simplex. J. Glob. Opt., 14:357–364.
    • (1999) J. Glob. Opt , vol.14 , pp. 357-364
    • Nowak, I.1
  • 144
    • 0347372718 scopus 로고    scopus 로고
    • Dual bounds and optimality cuts for all-quadratic programs with convex constraints
    • Nowak, I. (2000). Dual bounds and optimality cuts for all-quadratic programs with convex constraints. J. Glob. Opt., 18:337–356.
    • (2000) J. Glob. Opt , vol.18 , pp. 337-356
    • Nowak, I.1
  • 145
    • 28244446267 scopus 로고    scopus 로고
    • Lagrangian Decomposition of Block-Separable Mixed-Integer All-Quadratic Programs
    • Online First
    • Nowak, I. (2004). Lagrangian Decomposition of Block-Separable Mixed-Integer All-Quadratic Programs. Math. Progr., Online First:1–18.
    • (2004) Math. Progr , pp. 1-18
    • Nowak, I.1
  • 146
    • 0242543469 scopus 로고    scopus 로고
    • LaGO-An object oriented library for solving MINLPs
    • Bliek, C., Jermann, C., and Neumaier, A., editors, pages Springer, Berlin
    • Nowak, I., Alperin, H., and Vigerske, S. (2003). LaGO-An object oriented library for solving MINLPs. In Bliek, C., Jermann, C., and Neumaier, A., editors, Global Optimization and Constraint Satisfaction, pages 32–42. Springer, Berlin. http://www.mathematik.hu-berlin.de/~eopt/papers/LaGO.pdf.
    • (2003) Global Optimization and Constraint Satisfaction , pp. 32-42
    • Nowak, I.1    Alperin, H.2    Vigerske, S.3
  • 147
    • 0042230796 scopus 로고    scopus 로고
    • Stochastic Lagrangian relaxation applied to power scheduling in a hydro-thermal system under uncertainty
    • Nowak, M. P. and Römisch, W. (2000). Stochastic Lagrangian relaxation applied to power scheduling in a hydro-thermal system under uncertainty. An. Oper. Res., 100:251–272.
    • (2000) An. Oper. Res , vol.100 , pp. 251-272
    • Nowak, M. P.1    Römisch, W.2
  • 149
    • 0026124209 scopus 로고
    • A Branch-and-Cut algorithm for the resolution of large scale traveling salesman problems
    • Padberg, M. and Rinaldi, G. (1991). A Branch-and-Cut algorithm for the resolution of large scale traveling salesman problems. SIAM Review, 33:60–10.
    • (1991) SIAM Review , vol.33 , pp. 60-10
    • Padberg, M.1    Rinaldi, G.2
  • 152
    • 0039361444 scopus 로고
    • Quadratically constrained quadratic programming: Some applications and a method for solution
    • Phan-huy-Hao, E. (1982). Quadratically constrained quadratic programming: Some applications and a method for solution. ZOR, 26:105–119.
    • (1982) ZOR , vol.26 , pp. 105-119
    • Phan-huy-Hao, E.1
  • 154
    • 0000034070 scopus 로고
    • A Quadratic Assignment Formulation of the Molecular Conformation Problem
    • Phillips, A. T. and Rosen, J. B. (1994). A Quadratic Assignment Formulation of the Molecular Conformation Problem. J. Glob. Opt., 4:229–241.
    • (1994) J. Glob. Opt , vol.4 , pp. 229-241
    • Phillips, A. T.1    Rosen, J. B.2
  • 155
    • 0348117790 scopus 로고
    • A method for solving D.C. programming problems, Application to fuel mixture nonconvex optimization problems
    • Phing, T. Q., Tao, P. D., and An, L. T. H. (1994). A method for solving D.C. programming problems, Application to fuel mixture nonconvex optimization problems. J. Global Opt., 6:87–105.
    • (1994) J. Global Opt , vol.6 , pp. 87-105
    • Phing, T. Q.1    Tao, P. D.2    An, L. T. H.3
  • 156
    • 85093884334 scopus 로고    scopus 로고
    • Pintér, J. (2005). LGO. http://www.pinterconsulting.com.
    • (2005) LGO
    • Pintér, J.1
  • 158
    • 0002821681 scopus 로고
    • A recipe for semidefinite relaxation for (0,1)-quadratic programming
    • Poljak, S., Rendl, F., and Wolkowicz, H. (1995). A recipe for semidefinite relaxation for (0,1)-quadratic programming. J. Global Opt., 7(1):51–73.
    • (1995) J. Global Opt , vol.7 , Issue.1 , pp. 51-73
    • Poljak, S.1    Rendl, F.2    Wolkowicz, H.3
  • 159
    • 85049776636 scopus 로고
    • Optimization Software, Inc., Publications division
    • Polyak, B. T. (1987). Introduction to optimization. Optimization Software, Inc., Publications division.
    • (1987) Introduction to optimization
    • Polyak, B. T.1
  • 160
    • 0000686629 scopus 로고
    • A general method for solving extremum problems
    • Polyak, B. T. (1993). A general method for solving extremum problems. Soviet Mathematics, 8:593–597.
    • (1993) Soviet Mathematics , vol.8 , pp. 593-597
    • Polyak, B. T.1
  • 161
    • 0026932968 scopus 로고
    • An LP/NLP based branch and bound algorithm for convex MINLP optimization problems
    • Quesada, L. and Grossmann, I. E. (1992). An LP/NLP based branch and bound algorithm for convex MINLP optimization problems. Comp. Chem. Eng., 16:937–947.
    • (1992) Comp. Chem. Eng , vol.16 , pp. 937-947
    • Quesada, L.1    Grossmann, I. E.2
  • 163
    • 0003386697 scopus 로고
    • Interval Methods
    • Horst, R. and Pardalos, P., editors, pages Kluwer Academic Publishers, Dordrecht
    • Ratschek, H. and Rokne, J. (1995). Interval Methods. In Horst, R. and Pardalos, P., editors, Handbook of Global Optimization, pages 751–828. Kluwer Academic Publishers, Dordrecht.
    • (1995) Handbook of Global Optimization , pp. 751-828
    • Ratschek, H.1    Rokne, J.2
  • 164
    • 0028479001 scopus 로고
    • Some outer approximation methods for semi-infinite programming problems
    • Reemtsen, R. (1994). Some outer approximation methods for semi-infinite programming problems. J. Comp. Appl. Math., 53:87–108.
    • (1994) J. Comp. Appl. Math , vol.53 , pp. 87-108
    • Reemtsen, R.1
  • 165
    • 0031141179 scopus 로고    scopus 로고
    • A semidefinite framework for trust region subproblems with applications to large scale minimization
    • Rendl, F. and Wolkowicz, H. (1997). A semidefinite framework for trust region subproblems with applications to large scale minimization. Math. Progr., 77 (2):273–299.
    • (1997) Math. Progr , vol.77 , Issue.2 , pp. 273-299
    • Rendl, F.1    Wolkowicz, H.2
  • 166
    • 0012587086 scopus 로고    scopus 로고
    • Greedy randomized adaptive search procedures
    • Glover, F. and Kochenberger, G., editors, Kluwer Academic Publishers, Dordrecht
    • Resende, M. G. C. and Ribeiro, C. C. (2002). Greedy randomized adaptive search procedures. In Glover, F. and Kochenberger, G., editors, State-of-the-Art Handbook in Metaheuristics. Kluwer Academic Publishers, Dordrecht.
    • (2002) State-of-the-Art Handbook in Metaheuristics
    • Resende, M. G. C.1    Ribeiro, C. C.2
  • 167
    • 0016059769 scopus 로고
    • Augmented Lagrangian multiplier functions and duality in nonconvex programming
    • Rockafellar, R. T. (1974). Augmented Lagrangian multiplier functions and duality in nonconvex programming. SIAM J. Control, 12(2):268–285.
    • (1974) SIAM J. Control , vol.12 , Issue.2 , pp. 268-285
    • Rockafellar, R. T.1
  • 169
    • 0000365133 scopus 로고    scopus 로고
    • Decomposition methods in stochastic programming
    • Ruszczyński, A. (1997). Decomposition methods in stochastic programming. Math. Progr., 79:333–353.
    • (1997) Math. Progr , vol.79 , pp. 333-353
    • Ruszczyński, A.1
  • 170
    • 0037644377 scopus 로고
    • Product design: Sub-assemblies for multiple markets
    • Rutenberg, D. P. and Shaftel, T. L. (1971). Product design: Sub-assemblies for multiple markets. Management Science, 18:B220–B231.
    • (1971) Management Science , vol.18 , pp. B220-B231
    • Rutenberg, D. P.1    Shaftel, T. L.2
  • 171
    • 0000635160 scopus 로고    scopus 로고
    • A Branch-and-Reduce Approach to Global Optimization
    • Ryoo, H. S. and Sahinidis, N. (1996). A Branch-and-Reduce Approach to Global Optimization. J. Global Opt., 8:107–138.
    • (1996) J. Global Opt , vol.8 , pp. 107-138
    • Ryoo, H. S.1    Sahinidis, N.2
  • 172
    • 0000318768 scopus 로고    scopus 로고
    • BARON: A general purpose global optimization software package
    • Sahinidis, N. V. (1996). BARON: A general purpose global optimization software package. J. Global Opt., 8(2):201–205.
    • (1996) J. Global Opt , vol.8 , Issue.2 , pp. 201-205
    • Sahinidis, N. V.1
  • 174
    • 26644467962 scopus 로고    scopus 로고
    • Energy minimization by smoothing techniques: a survey
    • Balbuena, E. P. and Seminario, J., editors, pages Elsevier
    • Schelstraete, S., Schepens, W., and Verschelde, H. (1998). Energy minimization by smoothing techniques: a survey. In Balbuena, E. P. and Seminario, J., editors, From Classical to Quantum Methods, pages 129–185. Elsevier.
    • (1998) From Classical to Quantum Methods , pp. 129-185
    • Schelstraete, S.1    Schepens, W.2    Verschelde, H.3
  • 175
    • 21144458665 scopus 로고    scopus 로고
    • Habilitation Thesis, draft of a book, Cambridge Univ. Press, to appear
    • Schichl, H. (2004). Mathematical Modeling and Global Optimization. Habilitation Thesis, draft of a book, Cambridge Univ. Press, to appear.
    • (2004) Mathematical Modeling and Global Optimization
    • Schichl, H.1
  • 176
    • 28044471201 scopus 로고    scopus 로고
    • Interval analysis on directed acyclic graphs for global optimization
    • to appear
    • Schichl, H. and Neumaier, A. (2004). Interval analysis on directed acyclic graphs for global optimization. J. Global Optimization, to appear.
    • (2004) J. Global Optimization
    • Schichl, H.1    Neumaier, A.2
  • 179
    • 0042124553 scopus 로고
    • SCICON Ltd. Scicon Ltd., Milton Keynes, UK
    • SCICON Ltd. (1989). SCICONIC User Guide Version 1.40. Scicon Ltd., Milton Keynes, UK.
    • (1989) SCICONIC User Guide Version 1.40
  • 180
    • 0037236817 scopus 로고    scopus 로고
    • Constraint programming based lagrangian relaxation for the automatic recording problem
    • Sehlmann, M. and Fahle, T. (2003). Constraint programming based lagrangian relaxation for the automatic recording problem. An. Oper. Res., 118:17–33.
    • (2003) An. Oper. Res , vol.118 , pp. 17-33
    • Sehlmann, M.1    Fahle, T.2
  • 182
    • 0003374522 scopus 로고
    • A reformulation-convexification approach for solving nonconvex quadratic programming problems
    • Sherali, H. D. and Tuncbilek, C. H. (1995). A reformulation-convexification approach for solving nonconvex quadratic programming problems. J. Global Opt., 7:1–31.
    • (1995) J. Global Opt , vol.7 , pp. 1-31
    • Sherali, H. D.1    Tuncbilek, C. H.2
  • 183
    • 0023454146 scopus 로고
    • Quadratic optimization problems
    • Shor, N. Z. (1987). Quadratic optimization problems. Soviet J. Circ. Syst. Sci., 25, (6):1–11.
    • (1987) Soviet J. Circ. Syst. Sci , vol.25 , Issue.6 , pp. 1-11
    • Shor, N. Z.1
  • 184
    • 0002909079 scopus 로고
    • Dual estimates in multiextremal problems
    • Shor, N. Z. (1992). Dual estimates in multiextremal problems. J. Global Opt., 2:411–418.
    • (1992) J. Global Opt , vol.2 , pp. 411-418
    • Shor, N. Z.1
  • 186
    • 0000326858 scopus 로고    scopus 로고
    • Global optimization of general process models
    • Grossmann, I. E., editor, pages Kluwer Academic Publishers, Dordrecht
    • Smith, E. M. B. and Pantelides, C. C. (1996). Global optimization of general process models. In Grossmann, I. E., editor, Global Optimization in Engineering Design, pages 355–368. Kluwer Academic Publishers, Dordrecht.
    • (1996) Global Optimization in Engineering Design , pp. 355-368
    • Smith, E. M. B.1    Pantelides, C. C.2
  • 187
    • 0033134718 scopus 로고    scopus 로고
    • A Symbolic Reformulation/Spatial Branch and Bound Algorithm for the Global Optimization of nonconvex MINLPs
    • Smith, E. M. B. and Pantelides, C. C. (1999). A Symbolic Reformulation/Spatial Branch and Bound Algorithm for the Global Optimization of nonconvex MINLPs. Comp. Chem. Eng., 23:457–478.
    • (1999) Comp. Chem. Eng , vol.23 , pp. 457-478
    • Smith, E. M. B.1    Pantelides, C. C.2
  • 189
    • 0001219945 scopus 로고
    • Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations
    • Stern, R. and Wolkowicz, H. (1995). Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations. SIAM J. Opt., 5(2):286–313.
    • (1995) SIAM J. Opt , vol.5 , Issue.2 , pp. 286-313
    • Stern, R.1    Wolkowicz, H.2
  • 192
    • 0037616715 scopus 로고    scopus 로고
    • Global Optimization of Mixed Integer Nonlinear Programs: A Theoretical and Computational Study
    • to appear in pages
    • Tawarmalani, M. and Sahinidis, N. (1999). Global Optimization of Mixed Integer Nonlinear Programs: A Theoretical and Computational Study. to appear in Math. Progr., pages 1–70.
    • (1999) Math. Progr , pp. 1-70
    • Tawarmalani, M.1    Sahinidis, N.2
  • 196
    • 0030217802 scopus 로고    scopus 로고
    • Logic-based MINLP algorithms for Optimal Synthesis of Process Networks
    • Turkay, M. and Grossmann, I. E. (1996). Logic-based MINLP algorithms for Optimal Synthesis of Process Networks. Comp. Chem. Eng., 20(8):959–978.
    • (1996) Comp. Chem. Eng , vol.20 , Issue.8 , pp. 959-978
    • Turkay, M.1    Grossmann, I. E.2
  • 197
    • 0007861669 scopus 로고    scopus 로고
    • Global optimization of nonconvex MINLP’s by interval analysis
    • Grossmann, I. E., editor, pages Kluwer Academic Publishers, Dordrecht
    • Vaidyanathan, R. and EL-Halwagi, M. (1996). Global optimization of nonconvex MINLP’s by interval analysis. In Grossmann, I. E., editor, Global Optimization in Engineering Design, pages 175–193. Kluwer Academic Publishers, Dordrecht.
    • (1996) Global Optimization in Engineering Design , pp. 175-193
    • Vaidyanathan, R.1    EL-Halwagi, M.2
  • 198
    • 84863566939 scopus 로고    scopus 로고
    • Numerica: a modeling language for global optimization
    • Van Hentenryck, P. (1997). Numerica: a modeling language for global optimization. Proceedings of IJCAI’97.
    • (1997) Proceedings of IJCAI’97
    • Van Hentenryck, P.1
  • 201
    • 0002996592 scopus 로고
    • Complexity issues in global optimization: A survey
    • Horst, R. and Pardalos, P., editors, pages Kluwer Academic Publishers, Dordrecht
    • Vavasis, S. A. (1995). Complexity issues in global optimization: A survey. In Horst, R. and Pardalos, P., editors, Handbook of Global Optimization, pages 27–41. Kluwer Academic Publishers, Dordrecht.
    • (1995) Handbook of Global Optimization , pp. 27-41
    • Vavasis, S. A.1
  • 203
    • 0033134714 scopus 로고    scopus 로고
    • LOGMIP: A Disjunctive 0-1 Nonlinear Optimizer for Process System Models
    • Vecchietti, A. and Grossmann, I. E. (1999). LOGMIP: A Disjunctive 0-1 Nonlinear Optimizer for Process System Models. Comp. Chem. Eng., 23:555–565.
    • (1999) Comp. Chem. Eng , vol.23 , pp. 555-565
    • Vecchietti, A.1    Grossmann, I. E.2
  • 204
    • 0037443768 scopus 로고    scopus 로고
    • Modeling of discrete/continuous optimization problems: characterization and formulation of disjunctions and their relaxations
    • Vecchietti, A., Lee, S., and Grossmann, I. (2003). Modeling of discrete/continuous optimization problems: characterization and formulation of disjunctions and their relaxations. Comp. Chem. Eng., pages 433–448.
    • (2003) Comp. Chem. Eng , pp. 433-448
    • Vecchietti, A.1    Lee, S.2    Grossmann, I.3
  • 206
    • 0025459923 scopus 로고
    • A Combined Penalty Function and Outer-Approximation Method for MINLP Optimization
    • Viswanathan, J. and Grossmann, I. E. (1990). A Combined Penalty Function and Outer-Approximation Method for MINLP Optimization. Comp. Chem. Eng., 14:769.
    • (1990) Comp. Chem. Eng , vol.14 , pp. 769
    • Viswanathan, J.1    Grossmann, I. E.2
  • 207
    • 0025596333 scopus 로고
    • A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: II. Application of theory and test problems
    • Visweswaran, V. and Floudas, C. A. (1990). A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: II. Application of theory and test problems. Comp. Chem. Eng.
    • (1990) Comp. Chem. Eng
    • Visweswaran, V.1    Floudas, C. A.2
  • 208
    • 8744308573 scopus 로고    scopus 로고
    • Decomposition of mixed-integer optimal control problems using branch and bound and sparse direct collocation
    • Engell, S., Kowalewski, S., and Zaytoon, J., editors, pages Shaker-Verlag, Dortmund
    • von Stryk, O. and Glocker, M. (2000). Decomposition of mixed-integer optimal control problems using branch and bound and sparse direct collocation. In Engell, S., Kowalewski, S., and Zaytoon, J., editors, Proc. ADPM 2000-The 4th International Conference on Automation of Mixed Processes: Hybrid Dynamic Systems, pages 99–104. Shaker-Verlag, Dortmund.
    • (2000) Proc. ADPM 2000-The 4th International Conference on Automation of Mixed Processes: Hybrid Dynamic Systems , pp. 99-104
    • von Stryk, O.1    Glocker, M.2
  • 210
    • 0040820269 scopus 로고
    • A cutting plane approach for chance-constrained linear programs
    • Weintraub, A. and Vera, J. (1991). A cutting plane approach for chance-constrained linear programs. Operations Research, 39:776–785.
    • (1991) Operations Research , vol.39 , pp. 776-785
    • Weintraub, A.1    Vera, J.2
  • 212
    • 0029216437 scopus 로고
    • An extended cutting plane method for solving convex MINLP problems
    • Westerlund, T. and Petterson, F. (1995). An extended cutting plane method for solving convex MINLP problems. Comp. Chem. Eng., 21:131–136.
    • (1995) Comp. Chem. Eng , vol.21 , pp. 131-136
    • Westerlund, T.1    Petterson, F.2
  • 213
    • 0028501750 scopus 로고
    • Optimization of pump configuration problems as a MINLP problem
    • Westerlund, T., Petterson, F., and Grossmann, I. E. (1994). Optimization of pump configuration problems as a MINLP problem. Comp. Chem. Eng., 18(9):845– 858.
    • (1994) Comp. Chem. Eng , vol.18 , Issue.9 , pp. 845-858
    • Westerlund, T.1    Petterson, F.2    Grossmann, I. E.3
  • 214
    • 0031676324 scopus 로고    scopus 로고
    • An extended cutting plane method for a class of non-convex MINLP problems
    • Westerlund, T., Skrifvars, H., Harjunkoski, I., and Pörn, R. (1998). An extended cutting plane method for a class of non-convex MINLP problems. Comp. Chem. Eng., 22(3):357–365.
    • (1998) Comp. Chem. Eng , vol.22 , Issue.3 , pp. 357-365
    • Westerlund, T.1    Skrifvars, H.2    Harjunkoski, I.3    Pörn, R.4
  • 216
    • 0032216248 scopus 로고    scopus 로고
    • Continuous Global Optimization of Structured Process Systems Models
    • Zamora, J. M. and Grossmann, I. E. (1998a). Continuous Global Optimization of Structured Process Systems Models. Comp. Chem. Eng., 22(12):1749–1770.
    • (1998) Comp. Chem. Eng , vol.22 , Issue.12 , pp. 1749-1770
    • Zamora, J. M.1    Grossmann, I. E.2
  • 217
    • 0031810541 scopus 로고    scopus 로고
    • A Global MINLP Optimization Algorithm for the Synthesis of Heat Exchanger Networks with no Stream Splits
    • Zamora, J. M. and Grossmann, I. E. (1998b). A Global MINLP Optimization Algorithm for the Synthesis of Heat Exchanger Networks with no Stream Splits. Comp. Chem. Eng., 22(3):367–384.
    • (1998) Comp. Chem. Eng , vol.22 , Issue.3 , pp. 367-384
    • Zamora, J. M.1    Grossmann, I. E.2
  • 218
    • 0036250973 scopus 로고    scopus 로고
    • New bundle methods for solving lagrangian relaxation dual problems
    • Zhao, X. and Luh, B. P. (2002). New bundle methods for solving lagrangian relaxation dual problems. Journal of Optimization Theory and Applications, 113:373–397.
    • (2002) Journal of Optimization Theory and Applications , vol.113 , pp. 373-397
    • Zhao, X.1    Luh, B. P.2
  • 219
    • 0032631766 scopus 로고    scopus 로고
    • Outward rotations: a tool for rounding solutions of semidefinite programming relaxations, with applications to max cut and other problems
    • Zwick, U. (1999). Outward rotations: a tool for rounding solutions of semidefinite programming relaxations, with applications to max cut and other problems. In Proc. of 31th STOC, pages 679–687.
    • (1999) Proc. of 31th STOC , pp. 679-687
    • Zwick, U.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.