Optimality Conditions and Exact Penalty for Mathematical Programs with Switching Constraints

In this paper, we give an overview on optimality conditions and exact penalization for the mathematical program with switching constraints (MPSC). MPSC is a new class of optimization problems with important applications. It is well known that if MPSC is treated as a standard nonlinear program, some...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 190; no. 1; pp. 1 - 31
Main Authors Liang, Yan-Chao, Ye, Jane J.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.07.2021
Springer Nature B.V
Subjects
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Mathematical analysis
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Qualifications
Switching
Theory of Computation
Directional quasi-normality
Mathematical program with switching constraints
90C30
90C46
Mathematical program with disjunctive constraints
90C33
Directional optimality condition
Error bound
Exact penalization
Directional pseudo-normality
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Summary:In this paper, we give an overview on optimality conditions and exact penalization for the mathematical program with switching constraints (MPSC). MPSC is a new class of optimization problems with important applications. It is well known that if MPSC is treated as a standard nonlinear program, some of the usual constraint qualifications may fail. To deal with this issue, one could reformulate it as a mathematical program with disjunctive constraints (MPDC). In this paper, we first survey recent results on constraint qualifications and optimality conditions for MPDC, then apply them to MPSC. Moreover, we provide two types of sufficient conditions for the local error bound and exact penalty results for MPSC. One comes from the directional quasi-normality for MPDC, and the other is obtained via the local decomposition approach.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-021-01879-y