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Volumn 140, Issue 2, 2009, Pages 197-212

Solving bilevel linear programs using multiple objective linear programming

Author keywords

Bilevel linear programming; Efficient set; Multiple objective linear programming; Rational reaction set; Simplex algorithm pivot

Indexed keywords

LINEAR PROGRAMMING;

EID: 59349118709     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-008-9467-2     Document Type: Article
Times cited : (33)

References (30)
  • 5
    • 84874699429 scopus 로고    scopus 로고
    • Accessed20March2006
    • NEOS server for optimization, http://neos.mcs.anl.gov/neos. Accessed 20 March 2006
    • NEOS Server for Optimization
  • 6
    • 1542346047 scopus 로고    scopus 로고
    • Solving mathematical programs with complementarity constraints as nonlinear programs
    • R. Fletcher S. Leyffer 2004 Solving mathematical programs with complementarity constraints as nonlinear programs Optim. Methods Softw. 19 15 40
    • (2004) Optim. Methods Softw. , vol.19 , pp. 15-40
    • Fletcher, R.1    Leyffer, S.2
  • 7
    • 0019937742 scopus 로고
    • An explicit solution to the multi-level programming problem
    • J. Bard J. Falk 1982 An explicit solution to the multi-level programming problem Comput. Oper. Res. 9 77 100
    • (1982) Comput. Oper. Res. , vol.9 , pp. 77-100
    • Bard, J.1    Falk, J.2
  • 8
    • 0025502593 scopus 로고
    • A solution method for the linear static Stackelberg problem using penalty functions
    • G. Anandalingam D. White 1990 A solution method for the linear static Stackelberg problem using penalty functions IEEE Trans. Automat. Contr. 35 1170 1173
    • (1990) IEEE Trans. Automat. Contr. , vol.35 , pp. 1170-1173
    • Anandalingam, G.1    White, D.2
  • 9
    • 84989725893 scopus 로고
    • An algorithm for the discrete bilevel programming problem
    • J. Bard J. Moore 1992 An algorithm for the discrete bilevel programming problem Nav. Res. Logist. 39 419 435
    • (1992) Nav. Res. Logist. , vol.39 , pp. 419-435
    • Bard, J.1    Moore, J.2
  • 10
    • 0019608634 scopus 로고
    • A representation and economic interpretation of a two-level programming problem
    • J. Fortuny-Amat B. McCarl 1981 A representation and economic interpretation of a two-level programming problem J. Oper. Res. Soc. 32 783 792
    • (1981) J. Oper. Res. Soc. , vol.32 , pp. 783-792
    • Fortuny-Amat, J.1    McCarl, B.2
  • 11
    • 0000367326 scopus 로고
    • New branch-and-bound rules for linear bilevel programming
    • P. Hansen B. Jaumard G. Savard 1992 New branch-and-bound rules for linear bilevel programming SIAM J. Control Optim. 13 1194 1217
    • (1992) SIAM J. Control Optim. , vol.13 , pp. 1194-1217
    • Hansen, P.1    Jaumard, B.2    Savard, G.3
  • 12
    • 0023997843 scopus 로고
    • Existence of optimal solutions to mathematical programs with equilibrium constraints
    • P. Harker J. Pang 1988 Existence of optimal solutions to mathematical programs with equilibrium constraints Oper. Res. Lett. 7 61 64
    • (1988) Oper. Res. Lett. , vol.7 , pp. 61-64
    • Harker, P.1    Pang, J.2
  • 13
    • 33645434196 scopus 로고
    • A sequential LCP method for bilevel linear programming
    • J. Judice A. Faustino 1992 A sequential LCP method for bilevel linear programming Ann. Oper. Res. 34 89 106
    • (1992) Ann. Oper. Res. , vol.34 , pp. 89-106
    • Judice, J.1    Faustino, A.2
  • 17
    • 0007216405 scopus 로고
    • Finding efficient points for linear multiple objective programs
    • J. Ecker I. Kouada 1975 Finding efficient points for linear multiple objective programs Math. Program. 14 249 261
    • (1975) Math. Program. , vol.14 , pp. 249-261
    • Ecker, J.1    Kouada, I.2
  • 18
    • 84974858043 scopus 로고
    • On computing an initial efficient extreme point
    • 10
    • J. Ecker N. Hegner 1978 On computing an initial efficient extreme point J. Oper. Res. Soc. 29 10 1005 1007
    • (1978) J. Oper. Res. Soc. , vol.29 , pp. 1005-1007
    • Ecker, J.1    Hegner, N.2
  • 19
    • 0007216405 scopus 로고
    • Finding all efficient extreme points for multiple objective linear programs
    • J. Ecker I. Kouada 1978 Finding all efficient extreme points for multiple objective linear programs Math. Program. 14 249 261
    • (1978) Math. Program. , vol.14 , pp. 249-261
    • Ecker, J.1    Kouada, I.2
  • 20
    • 0025841208 scopus 로고
    • A note on the Pareto optimality of solutions to the linear bilevel programming problem
    • P. Marcotte G. Savard 1991 A note on the Pareto optimality of solutions to the linear bilevel programming problem Comput. Oper. Res. 18 355 359
    • (1991) Comput. Oper. Res. , vol.18 , pp. 355-359
    • Marcotte, P.1    Savard, G.2
  • 21
    • 33845656839 scopus 로고    scopus 로고
    • Multicriteria approach to bilevel optimization
    • J. Fliege L.N. Vicente 2006 Multicriteria approach to bilevel optimization J. Optim. Theory Appl. 131 209 225
    • (2006) J. Optim. Theory Appl. , vol.131 , pp. 209-225
    • Fliege, J.1    Vicente, L.N.2
  • 22
    • 0001053761 scopus 로고
    • Algorithms for the vector maximization problem
    • J. Philip 1972 Algorithms for the vector maximization problem Math. Program. 2 207 229
    • (1972) Math. Program. , vol.2 , pp. 207-229
    • Philip, J.1
  • 23
    • 0002393742 scopus 로고
    • An all linear programming relaxation algorithm for optimizing over the efficient set
    • H. Benson 1991 An all linear programming relaxation algorithm for optimizing over the efficient set J. Glob. Optim. 1 83 104
    • (1991) J. Glob. Optim. , vol.1 , pp. 83-104
    • Benson, H.1
  • 24
    • 0026853797 scopus 로고
    • A finite, nonadjacent extreme-point search algorithm for optimization over the efficient set
    • J. Benson 1992 A finite, nonadjacent extreme-point search algorithm for optimization over the efficient set J. Optim. Theory Appl. 73 47 64
    • (1992) J. Optim. Theory Appl. , vol.73 , pp. 47-64
    • Benson, J.1
  • 25
    • 0028713830 scopus 로고
    • Optimizing a linear function over the efficient set
    • J. Ecker J. Song 1994 Optimizing a linear function over the efficient set J. Optim. Theory Appl. 83 541 563
    • (1994) J. Optim. Theory Appl. , vol.83 , pp. 541-563
    • Ecker, J.1    Song, J.2
  • 26
    • 18144379490 scopus 로고    scopus 로고
    • A bilinear algorithm for optimizing a linear function over the efficient set of a multiple objective linear programming problem
    • J. Jorge 2005 A bilinear algorithm for optimizing a linear function over the efficient set of a multiple objective linear programming problem J. Glob. Optim. 31 1 16
    • (2005) J. Glob. Optim. , vol.31 , pp. 1-16
    • Jorge, J.1
  • 27
    • 0033716038 scopus 로고    scopus 로고
    • Optimizing over the efficient set using a top-down search of faces
    • S. Sayin 2000 Optimizing over the efficient set using a top-down search of faces Oper. Res. 48 65 72
    • (2000) Oper. Res. , vol.48 , pp. 65-72
    • Sayin, S.1
  • 28
    • 28244496090 scopus 로고    scopus 로고
    • Benchmarking optimization software with performance profiles
    • E. Dolan J. Moré 2002 Benchmarking optimization software with performance profiles Math. Program. 91 201 213
    • (2002) Math. Program. , vol.91 , pp. 201-213
    • Dolan, E.1    Moré, J.2
  • 29
    • 0022737275 scopus 로고
    • A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows
    • L. LeBlanc D. Boyce 1986 A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows Trans. Res. B 20B 259 265
    • (1986) Trans. Res. B , vol.20 , pp. 259-265
    • Leblanc, L.1    Boyce, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.