Is Pessimistic Bilevel Programming a Special Case of a Mathematical Program with Complementarity Constraints?

One of the most commonly used methods for solving bilevel programming problems (whose lower level problem is convex) starts with reformulating it as a mathematical program with complementarity constraints. This is done by replacing the lower level problem by its Karush–Kuhn–Tucker optimality conditi...

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Vydáno v:Journal of optimization theory and applications Ročník 181; číslo 2; s. 504 - 520
Hlavní autoři: Aussel, Didier, Svensson, Anton
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.05.2019
Springer Nature B.V
Springer Verlag
Témata:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Hierarchies
Mathematical analysis
Mathematical programming
Mathematics
Mathematics and Statistics
Minimax technique
Operations Research/Decision Theory
Optimization
Optimization and Control
Theory of Computation
Mathematical programming with complementarity constraints
Pessimistic approach
90C30
90C47
90C33
Bilevel problem
ISSN:0022-3239, 1573-2878
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Popis
Shrnutí:One of the most commonly used methods for solving bilevel programming problems (whose lower level problem is convex) starts with reformulating it as a mathematical program with complementarity constraints. This is done by replacing the lower level problem by its Karush–Kuhn–Tucker optimality conditions. The obtained mathematical program with complementarity constraints is (locally) solved, but the question of whether a solution of the reformulation yields a solution of the initial bilevel problem naturally arises. The question was first formulated and answered negatively, in a recent work of Dempe and Dutta, for the so-called optimistic approach. We study this question for the pessimistic approach also in the case of a convex lower level problem with a similar answer. Some new notions of local solutions are defined for these minimax-type problems, for which the relations are shown. Some simple counterexamples are given.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-018-01467-7