메뉴 건너뛰기




Volumn 47, Issue 4, 2010, Pages 615-637

Solving convex quadratic bilevel programming problems using an enumeration sequential quadratic programming algorithm

Author keywords

Convex quadratic bilevel program; Enumeration sequential quadratic programming algorithm; Monotonicity network; Primal dual monotonicity

Indexed keywords

BILEVEL PROGRAMMING PROBLEM; BILEVEL PROGRAMS; COMPUTATIONAL RESULTS; FEASIBLE REGIONS; FRAME-WORK; MONOTONICITY; MONOTONICITY PROPERTY; OBJECTIVE FUNCTIONS; OPTIMALITY CONDITIONS; OPTIMISTIC APPROACH; PRIMAL-DUAL; RATIONAL SOLUTION; SEQUENTIAL LINEAR PROGRAMMING; SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM;

EID: 77954758865     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-009-9482-3     Document Type: Article
Times cited : (29)

References (45)
  • 1
    • 38249035647 scopus 로고
    • Government-private sector relations as a stackelberg game: A degenerate case
    • doi:10.1016/S0165-1889 87 80004-0
    • Abdou-Kandil, H., Bertrand, P.: Government-private sector relations as a stackelberg game: a degenerate case. J. Econ. Dyn. Control 11, 513-517 (1987). doi:10.1016/S0165-1889 (87) 80004-0
    • (1987) J. Econ. Dyn. Control , vol.11 , pp. 513-517
    • Abdou-Kandil, H.1    Bertrand, P.2
  • 2
    • 0031532337 scopus 로고    scopus 로고
    • Links between linear bilevel and mixed 0-1 programming problems
    • doi:10.1023/A:1022645805569
    • Audet, C., Hansen, P., Jaumard, B., Savard, G.: Links between linear bilevel and mixed 0-1 programming problems. J. Optim. Theory Appl. 93 (2), 273-300 (1997). doi:10.1023/A:1022645805569
    • (1997) J. Optim. Theory Appl. , vol.93 , Issue.2 , pp. 273-300
    • Audet, C.1    Hansen, P.2    Jaumard, B.3    Savard, G.4
  • 3
    • 0001454730 scopus 로고
    • A branch and bound algorithm for the bilevel programming problem
    • doi:10.1137/0911017
    • Bard, J. F., Moore, J. T.: A branch and bound algorithm for the bilevel programming problem. SIAM J. Sci. Stat. Comput. 11, 281-292 (1990). doi:10.1137/0911017
    • (1990) SIAM J. Sci. Stat. Comput. , vol.11 , pp. 281-292
    • Bard, J.F.1    Moore, J.T.2
  • 4
    • 0023843286 scopus 로고
    • Convex two-level programming
    • doi:10.1007/BF01580720
    • Bard, J. F.: Convex two-level programming. Math. Program. 40 (1), 15-28 (1988). doi:10.1007/BF01580720
    • (1988) Math. Program , vol.40 , Issue.1 , pp. 15-28
    • Bard, J.F.1
  • 5
    • 0021386336 scopus 로고
    • Optimality conditions for the bilevel programming problem
    • doi:10.1002/nav. 3800310104
    • Bard, J. F.: Optimality conditions for the bilevel programming problem. Nav. Res. Logist. Q. 31, 13-26 (1984). doi:10.1002/nav. 3800310104
    • (1984) Nav. Res. Logist. Q , vol.31 , pp. 13-26
    • Bard, J.F.1
  • 6
    • 0001926137 scopus 로고    scopus 로고
    • A bilevel programming approach to determining tax credits for biofuel production
    • doi:10.1016/S0377-2217 98 00373-7
    • Bard, J. F., Plummer, J. C., Sourie, J. C.: A bilevel programming approach to determining tax credits for biofuel production. Eur. J. Oper. Res. 120, 30-43 (2000). doi:10.1016/S0377-2217 (98) 00373-7
    • (2000) Eur. J. Oper. Res. , vol.120 , pp. 30-43
    • Bard, J.F.1    Plummer, J.C.2    Sourie, J.C.3
  • 7
    • 0025431821 scopus 로고
    • Computational difficulties of bilevel linear programming
    • doi:10.1287/opre.38.3.556
    • Ben-Ayed, O., Blair, C.: Computational difficulties of bilevel linear programming. Oper. Res. 38, 556-560 (1990). doi:10.1287/opre.38.3.556
    • (1990) Oper. Res. , vol.38 , pp. 556-560
    • Ben-Ayed, O.1    Blair, C.2
  • 8
    • 0346674567 scopus 로고
    • Procédures de résolution pour une classe de problème pouvant avoir un caractère combinatoire
    • Bertier, P., Roy, B.: Procédures de résolution pour une classe de problème pouvant avoir un caractère combinatoire. Cahier du centre d'études de recherche opérationnelle, 6 (1964)
    • (1964) Cahier du Centre D'études de Recherche opérationnelle , pp. 6
    • Bertier, P.1    Roy, B.2
  • 9
    • 0021479189 scopus 로고
    • Two-level linear programming
    • doi:10.1287/mnsc.30.8.1004
    • Bialas, W. F., Karwan, M. H.: Two-level linear programming. Manage. Sci. 30 (8), 1004-1020 (1984). doi:10.1287/mnsc.30.8.1004
    • (1984) Manage. Sci. , vol.30 , Issue.8 , pp. 1004-1020
    • Bialas, W.F.1    Karwan, M.H.2
  • 10
    • 0034245218 scopus 로고    scopus 로고
    • A bilevel model and solution algorithm for a freight tariff setting problem
    • doi:10.1287/trsc.34.3.289.12299
    • Brotcorne, L., Labbé, M., Marcotte, P., Savard, G.: A bilevel model and solution algorithm for a freight tariff setting problem. Transp. Sci. 34, 289-302 (2000). doi:10.1287/trsc.34.3.289.12299
    • (2000) Transp. Sci. , vol.34 , pp. 289-302
    • Brotcorne, L.1    Labbé, M.2    Marcotte, P.3    Savard, G.4
  • 11
    • 22044442312 scopus 로고    scopus 로고
    • On the quasiconcave bilevel programming problem
    • doi:10.1023/A:1022624029539
    • Calvete, H. I., Gale, C.: On the quasiconcave bilevel programming problem. J. Optim. Theory Appl. 98 (3), 613-622 (1998). doi:10.1023/A: 1022624029539
    • (1998) J. Optim. Theory Appl. , vol.98 , Issue.3 , pp. 613-622
    • Calvete, H.I.1    Gale, C.2
  • 12
    • 18344418693 scopus 로고    scopus 로고
    • A note on a penalty function approach for solving bilevel linear programs
    • doi:10.1023/A:1008308218364
    • Campêlo, M., Dantas, S., Scheimberg, S.: A note on a penalty function approach for solving bilevel linear programs. J. Glob. Optim. 16, 245-255 (2000). doi:10.1023/A:1008308218364
    • (2000) J. Glob. Optim. , vol.16 , pp. 245-255
    • Campêlo, M.1    Dantas, S.2    Scheimberg, S.3
  • 14
    • 0041635347 scopus 로고
    • World bank development research center discussion paper, Washington, January
    • Candler, W., Norton, R.: Multi-level programming. World bank development research center discussion paper, vol. 20, Washington, January (1977a)
    • (1977) Multi-level Programming , vol.20
    • Candler, W.1    Norton, R.2
  • 15
    • 0019912208 scopus 로고
    • Alinear two-level programming problem
    • doi:10.1016/0305-0548 82 90006-5
    • Candler, W., Townsley, R.: Alinear two-level programming problem. Comput. Oper. Res. 9, 57-76 (1982). doi:10.1016/0305-0548 (82) 90006-5
    • (1982) Comput. Oper. Res. , vol.9 , pp. 57-76
    • Candler, W.1    Townsley, R.2
  • 16
    • 84863041059 scopus 로고
    • The nonlinear bilevel programming problem: Formulation, regularity and optimality conditions
    • doi:10.1080/02331939508844048
    • Chen, Y., Florian, M.: The nonlinear bilevel programming problem: formulation, regularity and optimality conditions. Optimization 32, 193-309 (1995). doi:10.1080/02331939508844048
    • (1995) Optimization , vol.32 , pp. 193-309
    • Chen, Y.1    Florian, M.2
  • 17
    • 0009110583 scopus 로고
    • On cayley's formula for counting trees
    • doi:10. 1017/S0305004100037178
    • Clarke, L. E.: On cayley's formula for counting trees. Proc. Camb. Philos. Soc. 59, 509-517 (1963). doi:10. 1017/S0305004100037178
    • (1963) Proc. Camb. Philos. Soc. , vol.59 , pp. 509-517
    • Clarke, L.E.1
  • 19
    • 0010136361 scopus 로고
    • A simple algorithm for the linear bilevel programming problem
    • doi:10.1080/02331938708843247
    • Dempe, S.: A simple algorithm for the linear bilevel programming problem. Optimization 18, 373-385 (1987). doi:10.1080/02331938708843247
    • (1987) Optimization , vol.18 , pp. 373-385
    • Dempe, S.1
  • 20
    • 0000008666 scopus 로고
    • A necessary and sufficient optimality for bilevel programming problem
    • doi:10.1080/02331939208843831
    • Dempe, S.: A necessary and sufficient optimality for bilevel programming problem. Optimization 2, 341-354 (1992). doi:10.1080/02331939208843831
    • (1992) Optimization , vol.2 , pp. 341-354
    • Dempe, S.1
  • 21
    • 0042737841 scopus 로고    scopus 로고
    • Annoted bibliography on bilevel programming and mathematical programs with equilibrium constraints
    • doi:10.1080/0233193031000149894
    • Dempe, S.: Annoted bibliography on bilevel programming and mathematical programs with equilibrium constraints. Optimization 52, 333-359 (2003). doi:10.1080/0233193031000149894
    • (2003) Optimization , vol.52 , pp. 333-359
    • Dempe, S.1
  • 23
    • 0032244001 scopus 로고    scopus 로고
    • On the accurate identification of active constraints
    • doi:10.1137/S1052623496305882
    • Facchinei, F., Fischer, A., Kanzow, C.: On the accurate identification of active constraints. SIAM J. Optim. 9, 14-32 (1998). doi:10.1137/ S1052623496305882
    • (1998) SIAM J. Optim. , vol.9 , pp. 14-32
    • Facchinei, F.1    Fischer, A.2    Kanzow, C.3
  • 24
    • 0002423523 scopus 로고
    • On bilevel programming, part I: General nonlinear case
    • Falk, J. E., Liu, J.: On bilevel programming, part I: general nonlinear case. Math. Program. 70, 47-72 (1995)
    • (1995) Math. Program , vol.70 , pp. 47-72
    • Falk, J.E.1    Liu, J.2
  • 25
    • 0035332163 scopus 로고    scopus 로고
    • Global optimization of nonlinear bilevel programming problems
    • doi:10.1023/A:1011268113791
    • Gümüs, Z. H., Floudas, C. H.: Global optimization of nonlinear bilevel programming problems. J. Glob. Optim. 20, 1-31 (2001). doi:10.1023/A:1011268113791
    • (2001) J. Glob. Optim. , vol.20 , pp. 1-31
    • Gümüs, Z.H.1    Floudas, C.H.2
  • 26
    • 0024734703 scopus 로고
    • A frame work for algorithms in globally optimal design
    • Hansen, P., Jaumard, B., Lu, S. H.: A frame work for algorithms in globally optimal design. ASME J. Mech. Autom. Transm. 111, 353-360 (1989)
    • (1989) ASME J. Mech. Autom. Transm. , vol.111 , pp. 353-360
    • Hansen, P.1    Jaumard, B.2    Lu, S.H.3
  • 27
    • 0000367326 scopus 로고
    • New branch-and-bound rules for linear bilevel programming
    • doi:10.1137/0913069
    • Hansen, P., Jaumard, B., Savard, G.: New branch-and-bound rules for linear bilevel programming. SIAM J. Sci. Stat. Comput. 13, 1194-1217 (1992). doi:10.1137/0913069
    • (1992) SIAM J. Sci. Stat. Comput. , vol.13 , pp. 1194-1217
    • Hansen, P.1    Jaumard, B.2    Savard, G.3
  • 28
    • 0022077119 scopus 로고
    • The polynomial hierarchy and simple model for competitive analysis
    • doi:10.1007/BF01586088
    • Jeroslow, R. G.: The polynomial hierarchy and simple model for competitive analysis. Math. Program. 32, 146-164 (1985). doi:10.1007/BF01586088
    • (1985) Math. Program , vol.32 , pp. 146-164
    • Jeroslow, R.G.1
  • 29
    • 0025442309 scopus 로고
    • Derivative evaluation and computational experience with large bilevel mathematical programs
    • doi:10.1007/BF00939562
    • Kolstad, C. D., Lasdon, L.: Derivative evaluation and computational experience with large bilevel mathematical programs. J. Optim. Theory Appl. 65, 485-499 (1990). doi:10.1007/BF00939562
    • (1990) J. Optim. Theory Appl. , vol.65 , pp. 485-499
    • Kolstad, C.D.1    Lasdon, L.2
  • 30
    • 0040943685 scopus 로고
    • Two-level planning
    • doi:10.2307/1911892
    • Kornaj, J., Liptak, T.: Two-level planning. Econometrica 33, 141-169 (1965). doi:10.2307/1911892
    • (1965) Econometrica , vol.33 , pp. 141-169
    • Kornaj, J.1    Liptak, T.2
  • 31
    • 0032295962 scopus 로고    scopus 로고
    • A bilevel model of taxation and its application to optimal highway pricing
    • doi:10.1287/mnsc.44.12.1608
    • Labbé, M., Marcotte, P., Savard, G.: A bilevel model of taxation and its application to optimal highway pricing. Manage. Sci. 44, 1608-1622 (1998). doi:10.1287/mnsc.44.12.1608
    • (1998) Manage. Sci. , vol.44 , pp. 1608-1622
    • Labbé, M.1    Marcotte, P.2    Savard, G.3
  • 32
    • 10444236799 scopus 로고    scopus 로고
    • Hybrid algorithms with active set identification for mathematical programs with complementarity constraints
    • Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan
    • Lin, G. H., Fukushima, M.: Hybrid algorithms with active set identification for mathematical programs with complementarity constraints, Technical Report 2002-2008, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan (2003)
    • (2003) Technical Report 2002-2008
    • Lin, G.H.1    Fukushima, M.2
  • 35
    • 84867948361 scopus 로고    scopus 로고
    • A global optimization method for solving convex quadratic bilevel programming problems
    • doi:10.1023/A:1023047900333
    • Muu, L. D., Quy, N. V.: A global optimization method for solving convex quadratic bilevel programming problems. J. Glob. Optim. 26, 199-219 (2003). doi:10.1023/A:1023047900333
    • (2003) J. Glob. Optim. , vol.26 , pp. 199-219
    • Muu, L.D.1    Quy, N.V.2
  • 36
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton
    • Rockafellar, R. T.: Convex analysis. Princeton University Press, Princeton (1970)
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 37
    • 0000488805 scopus 로고
    • The economic theory of agency: The principal's problem
    • Ross, S. A.: The economic theory of agency: the principal's problem. AER 63, 134-139 (1973)
    • (1973) AER , vol.63 , pp. 134-139
    • Ross, S.A.1
  • 38
    • 0028444316 scopus 로고
    • The steepest descent direction for the nonlinear bilevel programming problem
    • doi:10.1016/0167-6377 94 90086-8
    • Savard, G., Gauvin, J.: The steepest descent direction for the nonlinear bilevel programming problem. Oper. Res. Lett. 1, 265-272 (1994). doi:10.1016/0167-6377 (94) 90086-8
    • (1994) Oper. Res. Lett. , vol.1 , pp. 265-272
    • Savard, G.1    Gauvin, J.2
  • 40
    • 0036609863 scopus 로고    scopus 로고
    • Linear bilevel problems: Genericity results and efficient method for computing local minima
    • doi:10.1007/s001860200189
    • Still, G.: Linear bilevel problems: genericity results and efficient method for computing local minima. Math. Methods Oper. Res. 5, 383-400 (2002). doi:10.1007/s001860200189
    • (2002) Math. Methods Oper. Res. , vol.5 , pp. 383-400
    • Still, G.1
  • 41
    • 0000527046 scopus 로고
    • Bilevel and multilevel programming, a bibliography review
    • doi:10.1007/BF01096458
    • Vicente, L. N., Calamai, P. H.: Bilevel and multilevel programming, a bibliography review. J. Glob. Optim. 5 (3), 291-306 (1994). doi:10.1007/ BF01096458
    • (1994) J. Glob. Optim. , vol.5 , Issue.3 , pp. 291-306
    • Vicente, L.N.1    Calamai, P.H.2
  • 42
    • 0028425698 scopus 로고
    • Descent approach for quadratic bilevel programming
    • doi:10.1007/BF02191670
    • Vicente, L. N., Savard, G., Jùdice, J.: Descent approach for quadratic bilevel programming. J. Optim. Theory Appl. 81, 379-399 (1994). doi:10.1007/BF02191670
    • (1994) J. Optim. Theory Appl. , vol.81 , pp. 379-399
    • Vicente, L.N.1    Savard, G.2    Jùdice, J.3
  • 43
    • 0042136140 scopus 로고
    • A hierarchical optimization model of resource allocation
    • doi:10.1080/02331939408843928
    • Wang, S., Lootsma, F. A.: A hierarchical optimization model of resource allocation. Optimization 28, 351-365 (1994). doi:10.1080/02331939408843928
    • (1994) Optimization , vol.28 , pp. 351-365
    • Wang, S.1    Lootsma, F.A.2
  • 45
    • 0016574410 scopus 로고
    • Monotonicity and dominance in optimal hydraulic cylinder design
    • Wilde, D.: Monotonicity and dominance in optimal hydraulic cylinder design. J. Eng. Ind. 97 (4), 13-26 (1975)
    • (1975) J. Eng. Ind. , vol.97 , Issue.4 , pp. 13-26
    • Wilde, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.