Necessary optimality conditions for a semivectorial bilevel problem under a partial calmness condition

In this paper, we are concerned with a semivectorial bilevel optimization problem Using a partial calmness suitable for bilevel semivectorial problems, we formulate its necessary optimality conditions. Our approach consists of reformulating our problem into a one level optimization problem using suc...

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Bibliographic Details
Published inOptimization Vol. 70; no. 9; pp. 1937 - 1957
Main Authors Dempe, Stephan, Abderrazzak Gadhi, Nazih, El idrissi, Mohammed, Hamdaoui, Khadija
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.09.2021
Taylor & Francis LLC
Subjects
Cones
Constraining
limiting normal cone
limiting subdifferential
optimality condition
Optimization
Partial calmness
Primary 90C29
Secondary 49K99
semivectorial bilevel program
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Summary:In this paper, we are concerned with a semivectorial bilevel optimization problem Using a partial calmness suitable for bilevel semivectorial problems, we formulate its necessary optimality conditions. Our approach consists of reformulating our problem into a one level optimization problem using successively the kth-objective weighted-constraint and the optimal value reformulation. Our main results are given in terms of the limiting subdifferentials and the limiting normal cones. Completely detailed first-order necessary optimality conditions are then derived in the smooth setting while using the generalized differentiation calculus of Mordukhovich.
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content type line 14
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2020.1763991