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Volumn 134, Issue 2, 2007, Pages 353-370

New branch-and-cut algorithm for bilevel linear programming

Author keywords

Bilevel linear programming; Branch and cut algorithms; Gomory cuts; Linear mixed 0 1 integer programming

Indexed keywords

BRANCH AND BOUND METHOD; LINEAR PROGRAMMING;

EID: 36048983724     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-007-9263-4     Document Type: Article
Times cited : (55)

References (29)
  • 4
    • 0022077119 scopus 로고
    • The polynomial hierarchy and a simple model for competitive analysis
    • Jeroslow, R.: The polynomial hierarchy and a simple model for competitive analysis. Math. Program. 32, 146-164 (1985)
    • (1985) Math. Program. , vol.32 , pp. 146-164
    • Jeroslow, R.1
  • 5
    • 0000367326 scopus 로고
    • New branch-and-bound rules for linear bilevel programming
    • Hansen, P., Jaumard, B., Savard, G.: New branch-and-bound rules for linear bilevel programming. SIAM J. Sci. Stat. Comput. 13, 1194-1217 (1992)
    • (1992) SIAM J. Sci. Stat. Comput. , vol.13 , pp. 1194-1217
    • Hansen, P.1    Jaumard, B.2    Savard, G.3
  • 8
    • 0344718017 scopus 로고    scopus 로고
    • Exact penalization of mathematical programs with equilibrium constraints
    • Scholtes, S., Stohr, M.: Exact penalization of mathematical programs with equilibrium constraints. SIAM J. Control Optim. 37, 617-652 (1999)
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 617-652
    • Scholtes, S.1    Stohr, M.2
  • 9
    • 0000181946 scopus 로고    scopus 로고
    • Complementarity constraint qualifications and simplified b-stationarity conditions for mathematical programs with equilibrium constraints
    • Fukushima, M., Pang, J.S.: Complementarity constraint qualifications and simplified b-stationarity conditions for mathematical programs with equilibrium constraints. Comput. Optim. Appl. 13, 111-136 (1999)
    • (1999) Comput. Optim. Appl. , vol.13 , pp. 111-136
    • Fukushima, M.1    Pang, J.S.2
  • 11
    • 0019912208 scopus 로고
    • A linear two-level programming problem
    • Candler, W., Townsley, R.: A linear two-level programming problem. Comput. Oper. Res. 9, 59-76 (1982)
    • (1982) Comput. Oper. Res. , vol.9 , pp. 59-76
    • Candler, W.1    Townsley, R.2
  • 12
    • 0021479189 scopus 로고
    • Two-level linear programming
    • Bialas, W., Karwan, M.: Two-level linear programming. Manag. Sci. 30, 1004-1020 (1984)
    • (1984) Manag. Sci. , vol.30 , pp. 1004-1020
    • Bialas, W.1    Karwan, M.2
  • 13
    • 0001915878 scopus 로고
    • A global optimization approach for the linear two-level program
    • Tuy, H., Migdalas, A., Värbrand, P.: A global optimization approach for the linear two-level program. J. Glob. Optim. 3, 1-23 (1993)
    • (1993) J. Glob. Optim. , vol.3 , pp. 1-23
    • Tuy, H.1    Migdalas, A.2    Värbrand, P.3
  • 14
    • 8344243145 scopus 로고
    • A parametric complementarity pivot approach for two-level linear programming
    • State University of New York at Buffalo
    • Bialas, W., Karwan, M., Shaw, J.: A parametric complementarity pivot approach for two-level linear programming. Operations Research Program Report 80-2, State University of New York at Buffalo (1980)
    • (1980) Operations Research Program Report , vol.80 , Issue.2
    • Bialas, W.1    Karwan, M.2    Shaw, J.3
  • 15
    • 33645434196 scopus 로고
    • A sequential LCP method for bilevel linear programming
    • Júdice, J., Faustino, A.: A sequential LCP method for bilevel linear programming. Ann. Oper. Res. 34, 89-106 (1992)
    • (1992) Ann. Oper. Res. , vol.34 , pp. 89-106
    • Júdice, J.1    Faustino, A.2
  • 16
    • 0001454730 scopus 로고
    • A branch-and-bound algorithm for the bilevel programming problem
    • Bard, J.F., Moore, J.: A branch-and-bound algorithm for the bilevel programming problem. SIAM J. Sci. Stat. Comp. 11, 281-292 (1990)
    • (1990) SIAM J. Sci. Stat. Comp. , vol.11 , pp. 281-292
    • Bard, J.F.1    Moore, J.2
  • 17
    • 0001553298 scopus 로고
    • Concave programming under linear constraints
    • Tuy, H.: Concave programming under linear constraints. Sov. Math. 5, 1437-1440 (1964)
    • (1964) Sov. Math. , vol.5 , pp. 1437-1440
    • Tuy, H.1
  • 18
    • 0000138482 scopus 로고
    • A penalty function approach for solving bilevel linear programs
    • White, D., 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.1    Anandalingam, G.2
  • 19
    • 36049023594 scopus 로고
    • A cutting-plane algorithm for the linear bilevel programming problem
    • Marcotte, P., Shiquan, W., Chen, Y.: A cutting-plane algorithm for the linear bilevel programming problem. CRT Report 925 (1993)
    • (1993) CRT Report , vol.925
    • Marcotte, P.1    Shiquan, W.2    Chen, Y.3
  • 20
    • 36048944583 scopus 로고    scopus 로고
    • New branch-and-cut algorithm for bilevel linear programming
    • GERAD
    • Audet, C., Savard, G., Zghal, W.: New branch-and-cut algorithm for bilevel linear programming. GERAD Report G-2004-13, GERAD (2004)
    • (2004) GERAD Report G-2004-13
    • Audet, C.1    Savard, G.2    Zghal, W.3
  • 22
    • 0031532337 scopus 로고    scopus 로고
    • Links between linear bilevel and mixed 0-1 programming problems
    • Audet, C., Hansen, P., Jaumard, B., Savard, G.: Links between linear bilevel and mixed 0-1 programming problems. J. Optim. Theory Appl. 93, 273-300 (1997)
    • (1997) J. Optim. Theory Appl. , vol.93 , pp. 273-300
    • Audet, C.1    Hansen, P.2    Jaumard, B.3    Savard, G.4
  • 23
    • 0019608634 scopus 로고
    • A representation and economic interpretation of a two-level programming problem
    • Fortuny-Amat, J., McCarl, B.: A representation and economic interpretation of a two-level programming problem. J. Oper. Res. Soc. 32, 783-792 (1981)
    • (1981) J. Oper. Res. Soc. , vol.32 , pp. 783-792
    • Fortuny-Amat, J.1    McCarl, B.2
  • 24
    • 0039067393 scopus 로고
    • Mixed integer programming by a branch-and-bound technique
    • Beale, E.M.L., Small, R.E.: Mixed integer programming by a branch-and-bound technique. Proc. 3rd IFIP Congress 2, 450-451 (1965)
    • (1965) Proc. 3rd IFIP Congress , vol.2 , pp. 450-451
    • Beale, E.M.L.1    Small, R.E.2
  • 28
    • 0024734703 scopus 로고
    • A framework for algorithms in globally optimal design
    • Hansen, P., Jaumard, B., Lu, S.H.: A framework for algorithms in globally optimal design. J. Mech. Trans. Autom. Des. 111, 353-360 (1989)
    • (1989) J. Mech. Trans. Autom. Des. , vol.111 , pp. 353-360
    • Hansen, P.1    Jaumard, B.2    Lu, S.H.3
  • 29
    • 0343137998 scopus 로고    scopus 로고
    • A symmetrical linear maxmin approach to disjoint bilinear programming
    • Audet, C., Hansen, P., Jaumard, B., Savard, G.: A symmetrical linear maxmin approach to disjoint bilinear programming. Math. Program. 85, 573-592 (1999)
    • (1999) Math. Program. , vol.85 , pp. 573-592
    • Audet, C.1    Hansen, P.2    Jaumard, B.3    Savard, G.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.