On Frèchet normal cone for nonsmooth mathematical programming problems with switching constraints

IF 1.8 4区管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Rairo-Operations Research Pub Date : 2023-09-08 DOI:10.1051/ro/2023138

Balendu Bhooshan Upadhyay, Zahra Jafariani, Nader Kanzi, Maryam Naderi Parizi

引用次数: 0

Abstract

This paper is devoted to the study of a class of nonsmooth programming problems with switching constraints (abbreviated as, (NMPSC)), where all the involved functions in the switching constraints are assumed to be locally Lipschitz. We investigate the properties of Frèchet normal cone of (NMPSC). In particular, we introduce two Guignard type constraint qualifications for (NMPSC) in terms of Michel-Penot subdifferential. Moreover, we derive two estimates for the Fr‘echet normal cone of (NMPSC) and further establish stationarity conditions at an optimal solution for (NMPSC). To the best of our knowledge, this is for the first time Frèchet normal cone for (NMPSC) have been studied in the setting of Euclidean spaces.

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具有切换约束的非光滑数学规划问题的fr切法线锥

本文研究了一类具有切换约束的非光滑规划问题(简称NMPSC)，其中切换约束中所有涉及的函数都被假定为局部Lipschitz。研究了(NMPSC)的fr切法锥的性质。特别地，我们根据micheli - penot子微分引入了(NMPSC)的两个Guignard型约束条件。此外，我们得到了(NMPSC)的Fr ' cheet法锥的两个估计，并进一步建立了(NMPSC)最优解的平稳性条件。据我们所知，这是第一次在欧几里得空间中研究(NMPSC)的fr切法向锥。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Rairo-Operations Research 管理科学-运筹学与管理科学

CiteScore

3.60

自引率

22.20%

发文量

206

审稿时长

>12 weeks

期刊介绍： RAIRO-Operations Research is an international journal devoted to high-level pure and applied research on all aspects of operations research. All papers published in RAIRO-Operations Research are critically refereed according to international standards. Any paper will either be accepted (possibly with minor revisions) either submitted to another evaluation (after a major revision) or rejected. Every effort will be made by the Editorial Board to ensure a first answer concerning a submitted paper within three months, and a final decision in a period of time not exceeding six months.