Optimality Conditions, Qualifications and Approximation Method for a Class of Non-Lipschitz Mathematical Programs with Switching Constraints

Jinman Lv, Zhenhua Peng and Zhongping Wan
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Jinman Lv: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
Zhenhua Peng: Department of Mathematics, School of Sciences, Nanchang University, Nanchang 330031, China
Zhongping Wan: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Mathematics, 2021, vol. 9, issue 22, 1-20

Abstract: In this paper, we consider a class of mathematical programs with switching constraints (MPSCs) where the objective involves a non-Lipschitz term. Due to the non-Lipschitz continuity of the objective function, the existing constraint qualifications for local Lipschitz MPSCs are invalid to ensure that necessary conditions hold at the local minimizer. Therefore, we propose some MPSC-tailored qualifications which are related to the constraints and the non-Lipschitz term to ensure that local minimizers satisfy the necessary optimality conditions. Moreover, we study the weak, Mordukhovich, Bouligand, strongly (W-, M-, B-, S-) stationay, analyze what qualifications making local minimizers satisfy the (M-, B-, S-) stationay, and discuss the relationship between the given MPSC-tailored qualifications. Finally, an approximation method for solving the non-Lipschitz MPSCs is given, and we show that the accumulation point of the sequence generated by the approximation method satisfies S-stationary under the second-order necessary condition and MPSC Mangasarian-Fromovitz (MF) qualification.

Keywords: switching constraint; stationary point; non-Lipschitz; optimality condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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