参数集优化问题的Levitin-Polyak适定性

IF 1.4 4区数学 Q1 MATHEMATICS

Carpathian Journal of Mathematics Pub Date : 2022-12-21 DOI:10.37193/cjm.2023.02.12

Biswajit Tahu, M. Dhingra, Shylendra Kumar

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引用次数: 0

摘要

本文的目的是引入参数集优化问题的Levitin$-$Polyak（简称LP）适定性的两个概念，逐点概念和全局概念。给出了参数集优化问题为LP适定的充要条件。根据近似解集序列的上Hausdorff收敛性和Painlev-{e}$-$Kuratowski收敛性，还建立了参数集优化问题的LP适定性的刻画。

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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Levitin-Polyak Well-Posedness for Parametric Set Optimization Problem

The aim of this paper is to introduce two notions of Levitin$-$Polyak (LP in short) well-posedness for a parametric set optimization problem, a pointwise and a global notion. Necessary and sufficient conditions for a parametric set optimization problem to be LP well-posed are given. Characterizations of LP well-posedness for a parametric set optimization problem in terms of upper Hausdorff convergence and Painlev\'{e}$-$Kuratowski convergence of sequences of approximate solution sets are also established.

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来源期刊

Carpathian Journal of Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Carpathian Journal of Mathematics publishes high quality original research papers and survey articles in all areas of pure and applied mathematics. It will also occasionally publish, as special issues, proceedings of international conferences, generally (co)-organized by the Department of Mathematics and Computer Science, North University Center at Baia Mare. There is no fee for the published papers but the journal offers an Open Access Option to interested contributors.