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

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...

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Autores principales:	Jinman Lv, Zhenhua Peng, Zhongping Wan
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	switching constraint stationary point non-Lipschitz optimality condition Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/9b1e7273766c4bb195ba461be4317224
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spelling	oai:doaj.org-article:9b1e7273766c4bb195ba461be43172242021-11-25T18:17:10ZOptimality Conditions, Qualifications and Approximation Method for a Class of Non-Lipschitz Mathematical Programs with Switching Constraints10.3390/math92229152227-7390https://doaj.org/article/9b1e7273766c4bb195ba461be43172242021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2915https://doaj.org/toc/2227-7390In 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.Jinman LvZhenhua PengZhongping WanMDPI AGarticleswitching constraintstationary pointnon-Lipschitzoptimality conditionMathematicsQA1-939ENMathematics, Vol 9, Iss 2915, p 2915 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	switching constraint stationary point non-Lipschitz optimality condition Mathematics QA1-939
spellingShingle	switching constraint stationary point non-Lipschitz optimality condition Mathematics QA1-939 Jinman Lv Zhenhua Peng Zhongping Wan Optimality Conditions, Qualifications and Approximation Method for a Class of Non-Lipschitz Mathematical Programs with Switching Constraints
description	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.
format	article
author	Jinman Lv Zhenhua Peng Zhongping Wan
author_facet	Jinman Lv Zhenhua Peng Zhongping Wan
author_sort	Jinman Lv
title	Optimality Conditions, Qualifications and Approximation Method for a Class of Non-Lipschitz Mathematical Programs with Switching Constraints
title_short	Optimality Conditions, Qualifications and Approximation Method for a Class of Non-Lipschitz Mathematical Programs with Switching Constraints
title_full	Optimality Conditions, Qualifications and Approximation Method for a Class of Non-Lipschitz Mathematical Programs with Switching Constraints
title_fullStr	Optimality Conditions, Qualifications and Approximation Method for a Class of Non-Lipschitz Mathematical Programs with Switching Constraints
title_full_unstemmed	Optimality Conditions, Qualifications and Approximation Method for a Class of Non-Lipschitz Mathematical Programs with Switching Constraints
title_sort	optimality conditions, qualifications and approximation method for a class of non-lipschitz mathematical programs with switching constraints
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/9b1e7273766c4bb195ba461be4317224
work_keys_str_mv	AT jinmanlv optimalityconditionsqualificationsandapproximationmethodforaclassofnonlipschitzmathematicalprogramswithswitchingconstraints AT zhenhuapeng optimalityconditionsqualificationsandapproximationmethodforaclassofnonlipschitzmathematicalprogramswithswitchingconstraints AT zhongpingwan optimalityconditionsqualificationsandapproximationmethodforaclassofnonlipschitzmathematicalprogramswithswitchingconstraints
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Optimality Conditions, Qualifications and Approximation Method for a Class of Non-Lipschitz Mathematical Programs with Switching Constraints

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