New branch-and-bound rules for linear bilevel programming

New branch-and-bound rules for linear bilevel programming

A new branch-and-bound algorithm for linear bilevel programming is proposed. Necessary optimality conditions expressed in terms of tightness of the follower's constraints are used to fathom or simplify subproblems, branch and obtain penalties similar to those used in mixed-integer programming....

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Veröffentlicht in:SIAM journal on scientific and statistical computing 1992-09, Vol.13 (5), p.1194-1217
Hauptverfasser: HANSEN, P, JAUMARD, B, SAVARD, G
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Applied sciences
Control theory
Cooperation
Electricity
Exact sciences and technology
Grants
Hierarchies
Integer programming
Mathematical programming
Operational research and scientific management
Operational research. Management science
Variables
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Zusammenfassung:A new branch-and-bound algorithm for linear bilevel programming is proposed. Necessary optimality conditions expressed in terms of tightness of the follower's constraints are used to fathom or simplify subproblems, branch and obtain penalties similar to those used in mixed-integer programming. Computational results are reported and compare favorably to those of previous methods. Problems with up to 150 constraints, 250 variables controlled by the leader, and 150 variables controlled by the follower have been solved.
ISSN:0196-5204
1064-8275
2168-3417
1095-7197
DOI:10.1137/0913069