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Volumn 38, Issue 4, 2007, Pages 527-554

A novel approach to Bilevel nonlinear programming

Author keywords

Bilevel convex programming; Bilevel linear programming; Bilevel nonlinear programming; Branch reduce and bound method; Leader and follower game; Monotonic optimization; Monotonicity cuts; Polyblock approximation

Indexed keywords

APPROXIMATION THEORY; GAME THEORY; LINEAR PROGRAMMING; OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING;

EID: 34250845890     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-006-9093-1     Document Type: Conference Paper
Times cited : (35)

References (42)
  • 1
    • 0020787066 scopus 로고
    • An efficient point algorithm for a linear two-stage optimization problem
    • Bard, J.F.: An efficient point algorithm for a linear two-stage optimization problem. Oper. Res. 31, 670-684 (1983)
    • (1983) Oper. Res , vol.31 , pp. 670-684
    • Bard, J.F.1
  • 2
    • 0023843286 scopus 로고
    • Convex two-level optimization
    • Bard, J.F.: Convex two-level optimization. Math. Program. 40, 15-27 (1988)
    • (1988) Math. Program , vol.40 , pp. 15-27
    • Bard, J.F.1
  • 4
    • 0019937742 scopus 로고
    • An explicit solution to the multi-level programming problem
    • Bard, J.F., Falk, J.: An explicit solution to the multi-level programming problem. Comp. Oper. Res. 9, 77-100 (1982)
    • (1982) Comp. Oper. Res , vol.9 , pp. 77-100
    • Bard, J.F.1    Falk, J.2
  • 5
    • 0001900982 scopus 로고
    • Biological and synthetic hierarchical composites
    • Baer, E., Hiltner, A., Morgan, R.: Biological and synthetic hierarchical composites. Phys. Today 46, 60-67 (1992)
    • (1992) Phys. Today , vol.46 , pp. 60-67
    • Baer, E.1    Hiltner, A.2    Morgan, R.3
  • 6
    • 0027606149 scopus 로고
    • Bilevel linear programming
    • Ben-Ayed, O.: Bilevel linear programming. Comput. Oper. Res. 20, 485-501 (1993)
    • (1993) Comput. Oper. Res , vol.20 , pp. 485-501
    • Ben-Ayed, O.1
  • 8
    • 0009403492 scopus 로고
    • Mathematical programs with optimization problems in the constraints
    • Brackel, J., McGill, J.: Mathematical programs with optimization problems in the constraints. Oper. Res. 21, 37-44 (1973)
    • (1973) Oper. Res , vol.21 , pp. 37-44
    • Brackel, J.1    McGill, J.2
  • 9
    • 0043138174 scopus 로고
    • A method for solving mathematical programs with nonlinear programs in the constraints
    • Brackel, J., McGill, J.: A method for solving mathematical programs with nonlinear programs in the constraints. Oper. Res. 22, 1097-1101 (1974)
    • (1974) Oper. Res , vol.22 , pp. 1097-1101
    • Brackel, J.1    McGill, J.2
  • 10
    • 0019912208 scopus 로고    scopus 로고
    • Candler, W., Townsley, R.: A linear two-level programming problem. Comput. Ops Res. 9, 59-76 (1982)
    • Candler, W., Townsley, R.: A linear two-level programming problem. Comput. Ops Res. 9, 59-76 (1982)
  • 11
    • 0041635334 scopus 로고
    • Congested O-D trip emand adjustment problem: Bilevel programming formulation and optimality conditions
    • Migdalas, A, Pardalos, P, Värbrand, P, eds, Kluwer, Dordrecht
    • Chen, Y., Florian, M.: Congested O-D trip emand adjustment problem: bilevel programming formulation and optimality conditions. In: Migdalas, A., Pardalos, P., Värbrand, P. (eds.) Multilevel Optimization: Algorithms and Applications, pp. 1-22 Kluwer, Dordrecht (1988)
    • (1988) Multilevel Optimization: Algorithms and Applications , pp. 1-22
    • Chen, Y.1    Florian, M.2
  • 12
    • 84989695113 scopus 로고
    • A note on the optimality conditions for the bilevel programming problem
    • Clark, P.A., Westerberg, A.W.: A note on the optimality conditions for the bilevel programming problem. Naval Res. Logistics 35, 413-418 (1988)
    • (1988) Naval Res. Logistics , vol.35 , pp. 413-418
    • Clark, P.A.1    Westerberg, A.W.2
  • 13
    • 0007153962 scopus 로고
    • An implicit function approach to bilevel programming problems
    • Migdalas, A, Pardalos, P, Värbrand, P, eds, Kluwer, Dordrecht
    • Dempe, S.: An implicit function approach to bilevel programming problems. In: Migdalas, A., Pardalos, P., Värbrand, P. (eds.) Multilevel Optimization: Algorithms and Applications, pp. 273-289 Kluwer, Dordrecht (1988)
    • (1988) Multilevel Optimization: Algorithms and Applications , pp. 273-289
    • Dempe, S.1
  • 14
    • 0025841206 scopus 로고
    • Algorithms for nonlinear bilevel mathematical programming
    • Edmunds, T., Bard, J.: Algorithms for nonlinear bilevel mathematical programming. Trans. Syst. Man Cybernetics 21, 83-89 (1991)
    • (1991) Trans. Syst. Man Cybernetics , vol.21 , pp. 83-89
    • Edmunds, T.1    Bard, J.2
  • 15
    • 0002423523 scopus 로고
    • On bilevel programming, Part I; general nonlinear cases
    • Falk, J.E., Liu, J.: On bilevel programming, Part I; general nonlinear cases. Math. Program. 70, 47-72 (1995)
    • (1995) Math. Program , vol.70 , pp. 47-72
    • Falk, J.E.1    Liu, J.2
  • 17
    • 34250883719 scopus 로고    scopus 로고
    • On the equivalence between a linear bilevel programming problem and linear optimization over the efficient set
    • Computer and Automation Institute, Budapest
    • Fülöp, J.: On the equivalence between a linear bilevel programming problem and linear optimization over the efficient set. Working paper WP 93-1, LORDS, Computer and Automation Institute, Budapest
    • Working paper WP 93-1, LORDS
    • Fülöp, J.1
  • 18
    • 34250903422 scopus 로고    scopus 로고
    • Hansen, P., Jaumard, B., savard, G.: New branch and bound rules for linear bilevel programming. SIAMI Sci. Sta. Comput. 13, 1194-1217 (1992)
    • Hansen, P., Jaumard, B., savard, G.: New branch and bound rules for linear bilevel programming. SIAMI Sci. Sta. Comput. 13, 1194-1217 (1992)
  • 20
    • 0012055898 scopus 로고
    • Existence of solutions to generalized bilevel programming problem
    • Migdalas, A, Pardalos, P, Värbrand, P, eds, Kluwer, Dordrecht
    • Lignola, M.B., Morgan, J.: Existence of solutions to generalized bilevel programming problem. In: Migdalas, A., Pardalos, P., Värbrand, P. (eds.) Multilevel Optimization: Algorithms and Applications, pp. 315-330 Kluwer, Dordrecht (1988)
    • (1988) Multilevel Optimization: Algorithms and Applications , pp. 315-330
    • Lignola, M.B.1    Morgan, J.2
  • 21
    • 0042637157 scopus 로고
    • Quasiconvex lower level problem and applications to two level optimization
    • Springer, Dordrecht
    • Loridan, P., Morgan, J.: Quasiconvex lower level problem and applications to two level optimization. Lecture Notes in Economics and Mathematical Systems, vol. 345, pp. 325-341, Springer, Dordrecht (1990)
    • (1990) Lecture Notes in Economics and Mathematical Systems , vol.345 , pp. 325-341
    • Loridan, P.1    Morgan, J.2
  • 22
    • 0010134854 scopus 로고
    • Nonlinear bilevel problems with convex second level problem - heuristics and descent methods
    • Du, D.-Z, Zhang, X.-S, Cheng, K, eds, World Publishing Corporation, New York
    • Migdalas, A., Pardalos, P.M.: Nonlinear bilevel problems with convex second level problem - heuristics and descent methods. In: Du, D.-Z., Zhang, X.-S., Cheng, K., (eds.) Operations Research and Its Applications, pp. 194-204. World Publishing Corporation, New York (1995)
    • (1995) Operations Research and Its Applications , pp. 194-204
    • Migdalas, A.1    Pardalos, P.M.2
  • 23
    • 0037972915 scopus 로고    scopus 로고
    • Hierarchical and bilevel programming
    • Migdalas, A., Pardalos, P.M.: Hierarchical and bilevel programming. J. Glob. Optim. 8(3) (1996)
    • (1996) J. Glob. Optim , vol.8 , Issue.3
    • Migdalas, A.1    Pardalos, P.M.2
  • 24
    • 0003496903 scopus 로고    scopus 로고
    • Migdalas, A, Pardalos, P.M, Värbrand, P, eds, Kluwer, Dordrecht
    • Migdalas, A., Pardalos, P.M., Värbrand, P. (eds.): Multilevel Optimization: Algorithms and Applications. Kluwer, Dordrecht (1998)
    • (1998) Multilevel Optimization: Algorithms and Applications
  • 25
    • 0347487478 scopus 로고    scopus 로고
    • Complexity issues in hierarchical optimization
    • American Mathematical Society, pp, Providence, RI
    • Pardalos, P.M., Deng, X.: Complexity issues in hierarchical optimization. In: DIMACs series, vol. 37, American Mathematical Society, pp. 219-224. Providence, RI (1997)
    • (1997) DIMACs series , vol.37 , pp. 219-224
    • Pardalos, P.M.1    Deng, X.2
  • 27
    • 0043138061 scopus 로고    scopus 로고
    • Bilevel linear programming, multiobjective programming, and monotonic reverse convex programming
    • Migdalas, A, Pardalos, P.M, Värbrand, P, eds, Kluwer, Dordrecht
    • Tay, H.: Bilevel linear programming, multiobjective programming, and monotonic reverse convex programming. In: Migdalas, A., Pardalos, P.M., Värbrand, P. (eds.) Multilevel Optimization: Algorithms and Applications, pp. 295-314 Kluwer, Dordrecht (1998)
    • (1998) Multilevel Optimization: Algorithms and Applications , pp. 295-314
    • Tay, H.1
  • 29
    • 0001915878 scopus 로고    scopus 로고
    • Tay, H., Migdalas, A., Värbrand, P.: A global optimization approach for the linear two-level program. I Glob. Optim. 3, 1-23 (1992)
    • Tay, H., Migdalas, A., Värbrand, P.: A global optimization approach for the linear two-level program. I Glob. Optim. 3, 1-23 (1992)
  • 30
    • 0041635229 scopus 로고
    • A quasiconcave minimization method for solving linear two-level programs
    • Tuy, H., Migdalas, A., Värbrand, P.: A quasiconcave minimization method for solving linear two-level programs. J. Glob. Optim. 4, 243-263 (1994)
    • (1994) J. Glob. Optim , vol.4 , pp. 243-263
    • Tuy, H.1    Migdalas, A.2    Värbrand, P.3
  • 31
    • 0041635260 scopus 로고    scopus 로고
    • A new branch and bound method for bilevel linear programs
    • Migdalas, A, Pardalos, P.M, Värbrand, P, eds, Kluwer, Dordrecht
    • Tay, H., Ghannadan, s.: A new branch and bound method for bilevel linear programs. In: Migdalas, A., Pardalos, P.M., Värbrand, P. (eds.) Multilevel Optimization: Algorithms and Applications, pp. 231-249 Kluwer, Dordrecht (1998)
    • (1998) Multilevel Optimization: Algorithms and Applications , pp. 231-249
    • Tay, H.1    Ghannadan, S.2
  • 32
    • 0034353741 scopus 로고    scopus 로고
    • Monotonic optimization: Problems and solution approaches
    • Tuy, H.: Monotonic optimization: problems and solution approaches. SIAM J. Optim. 11, 464-494 (2000)
    • (2000) SIAM J. Optim , vol.11 , pp. 464-494
    • Tuy, H.1
  • 33
    • 0012043665 scopus 로고    scopus 로고
    • Convexity and monotonicity in global optimization
    • Hadjisavvas, N, Pardalos, P.M, eds, Kluwer, Dordrecht
    • Tay, H.: Convexity and monotonicity in global optimization. In: Hadjisavvas, N., Pardalos, P.M. (eds.) Advances in Convex Analysis and Optimization, pp. 569-594 Kluwer, Dordrecht (2001)
    • (2001) Advances in Convex Analysis and Optimization , pp. 569-594
    • Tay, H.1
  • 34
    • 34250833175 scopus 로고    scopus 로고
    • Hierarchical optimization
    • Pardalos, P, Resende, M, eds, Oxford University Press, Oxford
    • Tay, H.: Hierarchical optimization. In: Pardalos, P., Resende, M. (eds.) Handbook of Applied Optimization, pp. 502-513 Oxford University Press, Oxford (2002)
    • (2002) Handbook of Applied Optimization , pp. 502-513
    • Tay, H.1
  • 35
    • 34250854444 scopus 로고    scopus 로고
    • Monotonicity in the framework of generalized convexity
    • Eberhard, A, Hadjisavvas, N, Luc, D.T, eds, Springer, Berlin
    • Tay, H.: Monotonicity in the framework of generalized convexity. In: Eberhard, A., Hadjisavvas, N., Luc, D.T. (eds.) Generalized Convexity, Generalized Monotonicity and Applications, pp. 61-85 Springer, Berlin (2005)
    • (2005) Generalized Convexity, Generalized Monotonicity and Applications , pp. 61-85
    • Tay, H.1
  • 36
    • 84889991947 scopus 로고    scopus 로고
    • Monotonic Optimization: Branch and Cuts Methods
    • Audet, C, Hansen, P, Savard, G, eds, Springer, Berlin
    • Tay, H., Al-Khayyal, F., Thach, P.T.: Monotonic Optimization: Branch and Cuts Methods. In: Audet, C., Hansen, P., Savard, G. (eds.) Essays and Surveys on Global Optimization, pp. 39-78 Springer, Berlin (2005)
    • (2005) Essays and Surveys on Global Optimization , pp. 39-78
    • Tay, H.1    Al-Khayyal, F.2    Thach, P.T.3
  • 37
    • 84859270182 scopus 로고    scopus 로고
    • Optimization under composite monotonic constraints and constrained optimization over the efficient set
    • Liberti, L, Maculan, N, eds, Springer, Berlin
    • Tay, H., Hoai-Phuong, N.T.: Optimization under composite monotonic constraints and constrained optimization over the efficient set. In: Liberti, L., Maculan, N. (eds.) Global Optimization: from Theory to Implementation, pp. 3-31 Springer, Berlin (2006)
    • (2006) Global Optimization: From Theory to Implementation , pp. 3-31
    • Tay, H.1    Hoai-Phuong, N.T.2
  • 38
    • 0000527046 scopus 로고
    • Bilevel and multilevel programming: A bibliographic review
    • Vicente, L.N., Calamai, P.Y.: Bilevel and multilevel programming: a bibliographic review. J. Glob. Optim. 5, 291-306 (1994)
    • (1994) J. Glob. Optim , vol.5 , pp. 291-306
    • Vicente, L.N.1    Calamai, P.Y.2
  • 39
    • 0028425698 scopus 로고
    • Descent approaches for quadratic bilevel programming
    • Vicentee, L., Savard, G., Judice, J.: Descent approaches for quadratic bilevel programming. J. Optim. Theory Appl. 81, 379 (1994)
    • (1994) J. Optim. Theory Appl , vol.81 , pp. 379
    • Vicentee, L.1    Savard, G.2    Judice, J.3
  • 41
    • 0000138482 scopus 로고
    • A penalty function approach for solving bilevel linear programs
    • White, D.J., Anandalingam, G.: A penalty function approach for solving bilevel linear programs. J. Glob. Optim. 3, 397-419 (1993)
    • (1993) J. Glob. Optim , vol.3 , pp. 397-419
    • White, D.J.1    Anandalingam, G.2
  • 42
    • 0039272224 scopus 로고    scopus 로고
    • First-order necessary optimality conditions for general bilevel programming problems
    • Yezza, A.: First-order necessary optimality conditions for general bilevel programming problems. J Optim Theory Appl 89, 189-219 (1996)
    • (1996) J Optim Theory Appl , vol.89 , pp. 189-219
    • Yezza, A.1


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