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Optimality Conditions and Exact Penalty for Mathematical Programs with Switching Constraints

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Abstract

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.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

    Yan-Chao Liang

  2. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada

    Jane J. Ye

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  1. Yan-Chao Liang
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  2. Jane J. Ye
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Correspondence to Jane J. Ye.

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Communicated by Gianni Di Pillo.

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Y.-C. Liang work was supported in part by NSFC Grant #11801152, #12071133, #11671122. J. J. Ye work was supported by NSERC.

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Liang, YC., Ye, J.J. Optimality Conditions and Exact Penalty for Mathematical Programs with Switching Constraints. J Optim Theory Appl 190, 1–31 (2021). https://doi.org/10.1007/s10957-021-01879-y

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