Journal
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
Volume 181, Issue 2, Pages 504-520Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-018-01467-7
Keywords
Bilevel problem; Mathematical programming with complementarity constraints; Pessimistic approach
Funding
- FMJH Program Gaspard Monge in optimization and operation research
- EDF
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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.
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