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Volumn 20, Issue 1, 2001, Pages 1-31

Global Optimization of Nonlinear Bilevel Programming Problems

Author keywords

Bilevel nonlinear; Bilevel optimization; Bilevel programming; Global optimization; Mixed integer nonlinear optimization; Nonconvex; Twice continuously differentiable

Indexed keywords


EID: 0035332163     PISSN: 09255001     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1011268113791     Document Type: Article
Times cited : (134)

References (68)
  • 2
    • 0032552252 scopus 로고    scopus 로고
    • A Global Optimization Method, αBB, for General Twice-Differentiable Constrained NLPs II. Implementation and computational results
    • Adjiman, C.S., Androulakis, I.P. and Floudas, C.A. (1998b), 'A Global Optimization Method, αBB, for General Twice-Differentiable Constrained NLPs II. Implementation and computational results'. Comp. Chem. Engng. 22(9): 1159-1179.
    • (1998) Comp. Chem. Engng. , vol.22 , Issue.9 , pp. 1159-1179
    • Adjiman, C.S.1    Androulakis, I.P.2    Floudas, C.A.3
  • 3
    • 0034282316 scopus 로고    scopus 로고
    • Global Optimization of Mixed-Integer Nonlinear Problems
    • Adjiman, C.S., Androulakis, I.P. and Floudas, C.A. (2000), 'Global Optimization of Mixed-Integer Nonlinear Problems'. AIChE J. 46(9): 1769-1797.
    • (2000) AIChE J. , vol.46 , Issue.9 , pp. 1769-1797
    • Adjiman, C.S.1    Androulakis, I.P.2    Floudas, C.A.3
  • 4
    • 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. (1998a), 'A Global Optimization Method, αBB, for General Twice-Differentiable Constrained NLPs I. Theoretical Advances'. Comp. Chem. Engng. 22(9): 1137-1158.
    • (1998) Comp. Chem. Engng. , vol.22 , Issue.9 , pp. 1137-1158
    • Adjiman, C.S.1    Dallwig, S.2    Floudas, C.A.3    Neumaier, A.4
  • 5
    • 0003086747 scopus 로고    scopus 로고
    • Rigorous Convex Underestimators for General Twice-Differentiable Problems
    • Adjiman, C.S. and Floudas, C.A. (1996), Rigorous Convex Underestimators for General Twice-Differentiable Problems. Journal of Global Optimization 9: 23.
    • (1996) Journal of Global Optimization , vol.9 , pp. 23
    • Adjiman, C.S.1    Floudas, C.A.2
  • 6
    • 0019583841 scopus 로고    scopus 로고
    • Hierarchical decentralized systems and its solution by a barrier method
    • Aiyoshi, E. and Shimizu, K. (1996), Hierarchical decentralized systems and its solution by a barrier method. IEEE Trans. on Sys., Man., Cyb. 11(6): 444.
    • (1996) IEEE Trans. on Sys., Man., Cyb. , vol.11 , Issue.6 , pp. 444
    • Aiyoshi, E.1    Shimizu, K.2
  • 7
    • 0020752471 scopus 로고
    • Jointly Constrained Biconvex Programming
    • Al-Khayyal, F.A. and Falk, J.E. (1983), Jointly Constrained Biconvex Programming. Maths. Ops. Res. 8: 273.
    • (1983) Maths. Ops. Res. , vol.8 , pp. 273
    • Al-Khayyal, F.A.1    Falk, J.E.2
  • 8
    • 0001664372 scopus 로고
    • Global Optimization of concave functions subject to quadratic constraints: An application in nonlinear bilevel programming
    • P.P. M.
    • Al-Khayyal, F.A., Horst, R. and P.P. M., (1992), Global Optimization of concave functions subject to quadratic constraints: An application in nonlinear bilevel programming. Annals of Operations Research 34: 125.
    • (1992) Annals of Operations Research , vol.34 , pp. 125
    • Al-Khayyal, F.A.1    Horst, R.2
  • 9
    • 0033280779 scopus 로고    scopus 로고
    • A global optimization method for nonlinear bilevel programming problems
    • Amouzegar, M.A., (1999), A global optimization method for nonlinear bilevel programming problems. IEEE Trans. Syst., Man, Cyber. 29(6): 771-777.
    • (1999) IEEE Trans. Syst., Man, Cyber. , vol.29 , Issue.6 , pp. 771-777
    • Amouzegar, M.A.1
  • 10
    • 0025502593 scopus 로고
    • A solution method for the linear static Stackelberg problem using penalty functions
    • Anandalingam, G. and White, D.J. (1990), A solution method for the linear static Stackelberg problem using penalty functions. IEEE Trans. Auto. Contr. 35(10): 1170-1173.
    • (1990) IEEE Trans. Auto. Contr. , vol.35 , Issue.10 , pp. 1170-1173
    • Anandalingam, G.1    White, D.J.2
  • 11
  • 12
    • 0023843286 scopus 로고
    • Convex two-level optimization
    • Bard, J.F. (1988), Convex two-level optimization. Mathematical Programming 40: 15-27.
    • (1988) Mathematical Programming , vol.40 , pp. 15-27
    • Bard, J.F.1
  • 14
    • 0019937742 scopus 로고
    • An explicit solution to the multi-level programming problem
    • Bard, J.F. and Falk, J. (1982), An explicit solution to the multi-level programming problem. Comp. Op. Res. 9: 77-100.
    • (1982) Comp. Op. Res. , vol.9 , pp. 77-100
    • Bard, J.F.1    Falk, J.2
  • 16
    • 0002074385 scopus 로고    scopus 로고
    • Determining tax credits for converting non-food crops to biofuels: An application of bilevel programming
    • S.J. C., Migdalas, A., Pardalos, P.M. and Värbrand, P. (eds)
    • Bard, J.F., Plummer, J. and S.J. C., (1998), Determining tax credits for converting non-food crops to biofuels: an application of bilevel programming. In: Migdalas, A., Pardalos, P.M. and Värbrand, P. (eds), Multilevel Optimization: Algorithms and Applications, p. 23. Nonconvex Optimization and Its Applications, p. 23. Kluwer Academic Publishers, Dordrecht/Boston/London
    • (1998) Multilevel Optimization: Algorithms and Applications , pp. 23
    • Bard, J.F.1    Plummer, J.2
  • 17
    • 0004073418 scopus 로고    scopus 로고
    • Kluwer Academic Publishers, Dordrecht/Boston/London
    • Bard, J.F., Plummer, J. and S.J. C., (1998), Determining tax credits for converting non-food crops to biofuels: an application of bilevel programming. In: Migdalas, A., Pardalos, P.M. and Värbrand, P. (eds), Multilevel Optimization: Algorithms and Applications, p. 23. Nonconvex Optimization and Its Applications, p. 23. Kluwer Academic Publishers, Dordrecht/Boston/London
    • Nonconvex Optimization and Its Applications , pp. 23
  • 18
    • 0025431821 scopus 로고
    • Computational Difficulties of Bilevel Linear Programming
    • Ben-Ayed, O. and Blair, C.E. (1990), Computational Difficulties of Bilevel Linear Programming. Operations Research 38: 556-559.
    • (1990) Operations Research , vol.38 , pp. 556-559
    • Ben-Ayed, O.1    Blair, C.E.2
  • 19
    • 0024159073 scopus 로고
    • A general bilevel linear programming problem formulation of the network design problem
    • Ben-Ayed, O., Boyce, D.E. and Blair III, C.E. (1988), A general bilevel linear programming problem formulation of the network design problem. Trans. Res. 22B(4): 311.
    • (1988) Trans. Res. , vol.22 B , Issue.4 , pp. 311
    • Ben-Ayed, O.1    Boyce, D.E.2    Blair C.E. III3
  • 21
    • 0346226521 scopus 로고
    • A convex programming model for optimization problems in the constraints
    • Bracken, J. and McGill, J.T. (1973), A convex programming model for optimization problems in the constraints. Operations Research 21.
    • (1973) Operations Research , vol.21
    • Bracken, J.1    McGill, J.T.2
  • 22
    • 0026925611 scopus 로고
    • Coordinated design and control optimization of nonlinear processes
    • Brengel, D.D. and Seiderm, W. (1992), Coordinated design and control optimization of nonlinear processes. Comp. Chem. Engng. 16: 861-886.
    • (1992) Comp. Chem. Engng. , vol.16 , pp. 861-886
    • Brengel, D.D.1    Seiderm, W.2
  • 23
    • 0033115620 scopus 로고    scopus 로고
    • The bilevel linear/linear fractional programming problem
    • Calvete, H.J. and Gale, C. (1999), The bilevel linear/linear fractional programming problem. European Journal of Operational Research 114: 188-197.
    • (1999) European Journal of Operational Research , vol.114 , pp. 188-197
    • Calvete, H.J.1    Gale, C.2
  • 25
    • 0019912208 scopus 로고
    • A linear two-level programming problem
    • Candler, W. and Townsley, R. (1982), A linear two-level programming problem. Comp. Op. Res. 9(1).
    • (1982) Comp. Op. Res. , vol.9 , Issue.1
    • Candler, W.1    Townsley, R.2
  • 26
    • 0346890218 scopus 로고
    • Efficient distribution of resources through three levels of government
    • Cassidy, R.G., Kriby, M.J.L. and Raike, W.M. (1971), Efficient distribution of resources through three levels of government. Management Science 17(8): B-462.
    • (1971) Management Science , vol.17 , Issue.8
    • Cassidy, R.G.1    Kriby, M.J.L.2    Raike, W.M.3
  • 27
    • 0025116591 scopus 로고
    • Bilevel programming for steady-state chemical process design-I. Fundamentals and Algorithms
    • Clark, P.A. and Westerberg, A.W. (1990a), Bilevel programming for steady-state chemical process design-I. Fundamentals and Algorithms. Comp. Chem. Engng. 14(1): 87.
    • (1990) Comp. Chem. Engng. , vol.14 , Issue.1 , pp. 87
    • Clark, P.A.1    Westerberg, A.W.2
  • 28
    • 0025075580 scopus 로고
    • Bilevel programming for steady-state chemical process design-II. Performance study for nondegenerate designs
    • Clark, P.A. and Westerberg, A.W. (1990b), Bilevel programming for steady-state chemical process design-II. Performance study for nondegenerate designs. Comp. Chem. Engng. 14(1): 99.
    • (1990) Comp. Chem. Engng. , vol.14 , Issue.1 , pp. 99
    • Clark, P.A.1    Westerberg, A.W.2
  • 30
    • 0032069707 scopus 로고    scopus 로고
    • Global optimization in parameter estimation of nonlinear algebraic models via the error-in-variables Approach
    • Esposito, W.R. and Floudas, C.A. (1998), Global optimization in parameter estimation of nonlinear algebraic models via the error-in-variables Approach. Ind. Eng. Chem. Res. 37: 1841-1858.
    • (1998) Ind. Eng. Chem. Res. , vol.37 , pp. 1841-1858
    • Esposito, W.R.1    Floudas, C.A.2
  • 31
    • 0002423523 scopus 로고
    • On Bilevel Programming. 1. General Nonlinear Cases
    • Falk, J.E. and Liu, J. (1995), On Bilevel Programming. 1. General Nonlinear Cases. Mathematical Programming 70: 47-72.
    • (1995) Mathematical Programming , vol.70 , pp. 47-72
    • Falk, J.E.1    Liu, J.2
  • 32
    • 34250383688 scopus 로고
    • Sensitivity analysis for nonlinear programming using penalty methods
    • Fiacco, A.V. (1976), Sensitivity analysis for nonlinear programming using penalty methods. Maths. Prog. 10: 287.
    • (1976) Maths. Prog. , vol.10 , pp. 287
    • Fiacco, A.V.1
  • 33
    • 0141663368 scopus 로고    scopus 로고
    • Deterministic Global Optimization: Theory, Methods and Application
    • Kluwer Academic Publishers, Dordrecht, The Netherlands
    • Floudas, C.A. (2000), Deterministic Global Optimization: Theory, Methods and Application, Vol. 37 of Nonconvex Optimization and Its Applications. Kluwer Academic Publishers, Dordrecht, The Netherlands.
    • (2000) Nonconvex Optimization and Its Applications , vol.37
    • Floudas, C.A.1
  • 35
    • 0348117711 scopus 로고    scopus 로고
    • Optimality and duality in parametric convex lexicographic programming
    • Migdalas, A., Pardalos, P.M. and Värbrand, P. (eds), Multilevel Optimization: Algorithms and Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands
    • Floudas, C.A. and Zlobec, S. (1998), Optimality and duality in parametric convex lexicographic programming. In: Migdalas, A., Pardalos, P.M. and Värbrand, P. (eds), Multilevel Optimization: Algorithms and Applications, Vol. 20 of Nonconvex Optimization and Its Applications. Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 359-379.
    • (1998) Nonconvex Optimization and Its Applications , vol.20 , pp. 359-379
    • Floudas, C.A.1    Zlobec, S.2
  • 36
    • 0023537773 scopus 로고
    • Active constraint strategy for flexibility analysis in chemical processes
    • Grossmann, I.E. and Floudas, C.A. (1987), Active constraint strategy for flexibility analysis in chemical processes. Comp. Chem. Engng. 11(6): 675.
    • (1987) Comp. Chem. Engng. , vol.11 , Issue.6 , pp. 675
    • Grossmann, I.E.1    Floudas, C.A.2
  • 37
    • 0002964940 scopus 로고    scopus 로고
    • Reactive distillation column design with vapor/liquid/liquid equilibria
    • Gümüs, Z.H. and Ciric, A.R. (1997), Reactive distillation column design with vapor/liquid/liquid equilibria. Comp. Chem. Engng. 21(S): S983.
    • (1997) Comp. Chem. Engng. , vol.21 , Issue.S
    • Gümüs, Z.H.1    Ciric, A.R.2
  • 39
    • 0001099876 scopus 로고
    • A nonlinear bilevel model for analysis of electric utility demand-side planning issues
    • Hobbs, B.F. and Nelson, S.K. (1992), A nonlinear bilevel model for analysis of electric utility demand-side planning issues. Annals of Operations Research 34: 255.
    • (1992) Annals of Operations Research , vol.34 , pp. 255
    • Hobbs, B.F.1    Nelson, S.K.2
  • 40
    • 0000133803 scopus 로고    scopus 로고
    • Batch plant design and operations under uncertainty
    • Ierapetritou, M.G. and Pistikopoulos, E.N. (1996), Batch plant design and operations under uncertainty. I&EC Res. 35: 772.
    • (1996) I&EC Res. , vol.35 , pp. 772
    • Ierapetritou, M.G.1    Pistikopoulos, E.N.2
  • 41
    • 0010165388 scopus 로고
    • Double penalty method for bilevel optimization problems
    • Ishizuka, Y. and Aiyoshi, E. (1992), Double penalty method for bilevel optimization problems. Annals of Operations Research 34: 73-88.
    • (1992) Annals of Operations Research , vol.34 , pp. 73-88
    • Ishizuka, Y.1    Aiyoshi, E.2
  • 42
    • 0022077119 scopus 로고
    • The polynomial hierarchy and a simple model for competitive analysis
    • Jeroslow, R.G. (1985), The polynomial hierarchy and a simple model for competitive analysis. Math. Programming 32: 146.
    • (1985) Math. Programming , vol.32 , pp. 146
    • Jeroslow, R.G.1
  • 43
    • 0025464994 scopus 로고
    • Robust error-in-variables estimation using nonlinear programming techniques
    • Kim, I., Liebman, M.J. and Edgar, T.F. (1990), Robust error-in-variables estimation using nonlinear programming techniques. AIChE J. 36(7): 985-993.
    • (1990) AIChE J. , vol.36 , Issue.7 , pp. 985-993
    • Kim, I.1    Liebman, M.J.2    Edgar, T.F.3
  • 44
    • 23644452188 scopus 로고
    • A review of the literature on bilevel mathematical programming
    • US-32, Los Alamos National Lab.
    • Kolstad, C.D. (1985), A review of the literature on bilevel mathematical programming. Technical Report LA-10284-MS, US-32, Los Alamos National Lab.
    • (1985) Technical Report LA-10284-MS
    • Kolstad, C.D.1
  • 45
    • 0022737275 scopus 로고
    • A bilevel programming algorithm for exact solution of the network design problem with user optimal flows
    • LeBlanc, L.J. and Boyce, D.E. (1986), A bilevel programming algorithm for exact solution of the network design problem with user optimal flows. Trans. Res. B. 20B(3): 259.
    • (1986) Trans. Res. B. , vol.20 B , Issue.3 , pp. 259
    • LeBlanc, L.J.1    Boyce, D.E.2
  • 46
    • 0020114711 scopus 로고
    • Load adaptive pricing: An emerging tool for electric utilities
    • Luh, P.B., Ho, Y. and Muralidaran, R. (1982), Load adaptive pricing: an emerging tool for electric utilities. IEEE Trans. Auto. Contr. AC-27(2): 320.
    • (1982) IEEE Trans. Auto. Contr. , vol.AC-27 , Issue.2 , pp. 320
    • Luh, P.B.1    Ho, Y.2    Muralidaran, R.3
  • 48
    • 0010748018 scopus 로고
    • A Global Optimization Method for Weber's Problem with Attraction and Repulsion
    • Hager, W.W., Hearn, D.W. and Pardalos, P.M. (eds), Kluwer Academic Publishers, Dordrecht, The Netherlands
    • Maranas, C.D. and Floudas, C.A. (1994), A Global Optimization Method for Weber's Problem with Attraction and Repulsion. In: Hager, W.W., Hearn, D.W. and Pardalos, P.M. (eds), Large Scale Optimization: State of the Art. Kluwer Academic Publishers, Dordrecht, The Netherlands, p. 259.
    • (1994) Large Scale Optimization: State of the Art , pp. 259
    • Maranas, C.D.1    Floudas, C.A.2
  • 49
    • 34249758275 scopus 로고
    • Finding all solutions of nonlinearly constrained systems of equations
    • Maranas, C.D. and Floudas, C.A. (1995), Finding all solutions of nonlinearly constrained systems of equations. Journal of Global Optimization 7(2): 143-182.
    • (1995) Journal of Global Optimization , vol.7 , Issue.2 , pp. 143-182
    • Maranas, C.D.1    Floudas, C.A.2
  • 50
    • 0000248234 scopus 로고    scopus 로고
    • Exact and Inexact Penalty methods for the generalized bilevel programming problem
    • Marcotte, P. and Zhu, D.L. (1996), Exact and Inexact Penalty methods for the generalized bilevel programming problem. Mathematical Programming 74, 141-157.
    • (1996) Mathematical Programming , vol.74 , pp. 141-157
    • Marcotte, P.1    Zhu, D.L.2
  • 51
    • 0010087082 scopus 로고
    • Bilevel programming in traffic planning: Models, methods and challenge
    • Migdalas, A. (1995), Bilevel programming in traffic planning: models, methods and challenge. Journal of Global Optimization 7: 381.
    • (1995) Journal of Global Optimization , vol.7 , pp. 381
    • Migdalas, A.1
  • 52
    • 0003496903 scopus 로고    scopus 로고
    • Multilevel optimization: Algorithms and Applications
    • Kluwer Academic Publishers, Dordrecht, The Netherlands
    • Migdalas, A., Pardalos, P.M. and Värbrand, P. (1998), Multilevel optimization: Algorithms and Applications, Vol. 20 of Nonconvex Optimization and Its Applications. Kluwer Academic Publishers, Dordrecht, The Netherlands.
    • (1998) Nonconvex Optimization and Its Applications , vol.20
    • Migdalas, A.1    Pardalos, P.M.2    Värbrand, P.3
  • 53
    • 0029247427 scopus 로고
    • A multilevel analysis of agricultural credit dstribution in East Java, Indonesia
    • Onal, H., Darmawan, D.H. and Johnson III, S.H. (1995), A multilevel analysis of agricultural credit dstribution in East Java, Indonesia. Comp. Op. Res. 22(2): 227.
    • (1995) Comp. Op. Res. , vol.22 , Issue.2 , pp. 227
    • Onal, H.1    Darmawan, D.H.2    Johnson S.H. III3
  • 55
    • 0032535845 scopus 로고    scopus 로고
    • A dual temperature simulated annealing approach for solving bilevel programming problems
    • Sahin, K.H. and Ciric, A.R. (1998), A dual temperature simulated annealing approach for solving bilevel programming problems. Comp. Chem. Engng. 23: 11-25.
    • (1998) Comp. Chem. Engng. , vol.23 , pp. 11-25
    • Sahin, K.H.1    Ciric, A.R.2
  • 56
    • 0028444316 scopus 로고
    • The steepest descent direction for the nonlinear bilevel programming problem
    • Savard, G. and Gauvin, J. (1994), The steepest descent direction for the nonlinear bilevel programming problem. Operations Research Letters 15: 265-272.
    • (1994) Operations Research Letters , vol.15 , pp. 265-272
    • Savard, G.1    Gauvin, J.2
  • 60
  • 61
    • 0041635229 scopus 로고
    • A quasiconcave minimization method for solving linear two-level programs
    • Tuy, H., Migdalas, A. and Värbrand, P. (1993b), A quasiconcave minimization method for solving linear two-level programs. Journal of Global Optimization 4: 243.
    • (1993) Journal of Global Optimization , vol.4 , pp. 243
    • Tuy, H.1    Migdalas, A.2    Värbrand, P.3
  • 62
    • 0000527046 scopus 로고
    • Bilevel and Multilevel Programming: A bibliography review
    • Vicente, L. and Calamai, P. (1994), Bilevel and Multilevel Programming: A bibliography review. Journal of Global Optimization 5(2).
    • (1994) Journal of Global Optimization , vol.5 , Issue.2
    • Vicente, L.1    Calamai, P.2
  • 65
    • 0013633506 scopus 로고    scopus 로고
    • A decomposition-based global optimization approach for solving bilevel linear and quadratic programs
    • Floudas, C.A. and Pardalos, P.M. (eds), Kluwer Academic Publishers, Dordrecht, The Netherlands
    • Visweswaran, V., Floudas, C.A., Ierapetritou, M.G. and Pistikopoulos, E.N. (1996), A decomposition-based global optimization approach for solving bilevel linear and quadratic programs. In: Floudas, C.A. and Pardalos, P.M. (eds), State of the Art in Global Optimization, Nonconvex Optimization and its Applications. Kluwer Academic Publishers, Dordrecht, The Netherlands, p. 139.
    • (1996) State of the Art in Global Optimization, Nonconvex Optimization and Its Applications , pp. 139
    • Visweswaran, V.1    Floudas, C.A.2    Ierapetritou, M.G.3    Pistikopoulos, E.N.4
  • 67
    • 0000138482 scopus 로고
    • A penalty function approach for solving bilevel linear programs
    • White, D.J. and Anandalingam, G. (1993), A penalty function approach for solving bilevel linear programs. Journal of Global Optimization 3: 397-419.
    • (1993) Journal of Global Optimization , vol.3 , pp. 397-419
    • White, D.J.1    Anandalingam, G.2
  • 68
    • 0029271191 scopus 로고
    • Traffic Assignment and Signal Control in Saturated road networks
    • Yang, H. and Yagar, S. (1995), Traffic Assignment and Signal Control in Saturated road networks. Trans. Res. A. 29A(2): 125.
    • (1995) Trans. Res. A. , vol.29 A , Issue.2 , pp. 125
    • Yang, H.1    Yagar, S.2


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