强-弱凸规划问题解的表征

IF 0.8 4区数学 Q2 MATHEMATICS

Sbornik Mathematics Pub Date : 2021-01-01 DOI:10.1070/SM9431

S. Dudov, M. Osiptsev

{"title":"强-弱凸规划问题解的表征","authors":"S. Dudov, M. Osiptsev","doi":"10.1070/SM9431","DOIUrl":null,"url":null,"abstract":"Finite-dimensional problems of minimizing a strongly or weakly convex function on a strongly or weakly convex set are considered. Necessary and sufficient conditions for solutions of such problems are presented, which are based on estimates for the behaviour of the objective function on the feasible set taking account of the parameters of strong or weak convexity, as well as certain local features of the set and the function. The mathematical programming problem is considered separately for strongly and weakly convex functions. In addition, necessary conditions for a global and a local solution with differentiable objective function are found, in which a ‘strong’ stationarity condition is assumed to hold. Bibliography: 33 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Characterization of solutions of strong-weak convex programming problems\",\"authors\":\"S. Dudov, M. Osiptsev\",\"doi\":\"10.1070/SM9431\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Finite-dimensional problems of minimizing a strongly or weakly convex function on a strongly or weakly convex set are considered. Necessary and sufficient conditions for solutions of such problems are presented, which are based on estimates for the behaviour of the objective function on the feasible set taking account of the parameters of strong or weak convexity, as well as certain local features of the set and the function. The mathematical programming problem is considered separately for strongly and weakly convex functions. In addition, necessary conditions for a global and a local solution with differentiable objective function are found, in which a ‘strong’ stationarity condition is assumed to hold. Bibliography: 33 titles.\",\"PeriodicalId\":49573,\"journal\":{\"name\":\"Sbornik Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Sbornik Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1070/SM9431\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Sbornik Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1070/SM9431","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

研究了在强凸集或弱凸集上最小化强凸函数或弱凸函数的有限维问题。给出了这类问题解的充分必要条件，这些条件是基于考虑强凸或弱凸参数的目标函数在可行集上的行为估计，以及该集和函数的某些局部特征。分别考虑强凸函数和弱凸函数的数学规划问题。此外，还发现了目标函数可微的全局解和局部解存在的必要条件，并假设存在“强”平稳条件。参考书目:33种。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Characterization of solutions of strong-weak convex programming problems

Finite-dimensional problems of minimizing a strongly or weakly convex function on a strongly or weakly convex set are considered. Necessary and sufficient conditions for solutions of such problems are presented, which are based on estimates for the behaviour of the objective function on the feasible set taking account of the parameters of strong or weak convexity, as well as certain local features of the set and the function. The mathematical programming problem is considered separately for strongly and weakly convex functions. In addition, necessary conditions for a global and a local solution with differentiable objective function are found, in which a ‘strong’ stationarity condition is assumed to hold. Bibliography: 33 titles.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Sbornik Mathematics 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in: Mathematical analysis Ordinary differential equations Partial differential equations Mathematical physics Geometry Algebra Functional analysis