{"title":"Equivalence Relations in Convex Optimization","authors":"E. A. Nurminski","doi":"10.1134/S1990478923020126","DOIUrl":null,"url":null,"abstract":"<p> Several useful correspondences between general convex optimization problems, support\nfunctions, and projection operations are established. These correspondences cover the asymptotic\nequivalence of projection operations and computation of support functions for general convex sets,\nhence the same equivalence for general convex optimization problems, and the equivalence\nbetween least-norm problems and the problem of regularized convex suplinear optimization.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 2","pages":"339 - 344"},"PeriodicalIF":0.5800,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923020126","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
Several useful correspondences between general convex optimization problems, support
functions, and projection operations are established. These correspondences cover the asymptotic
equivalence of projection operations and computation of support functions for general convex sets,
hence the same equivalence for general convex optimization problems, and the equivalence
between least-norm problems and the problem of regularized convex suplinear optimization.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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