{"title":"The exact projective penalty method for constrained optimization","authors":"","doi":"10.1007/s10898-023-01350-4","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing its value at the projection of an infeasible point on the feasible set with the distance to the projection. Beside Euclidean projections, also a pointed projection in the direction of some fixed internal feasible point can be used. The equivalence means that local and global minimums of the problems coincide. Nonconvex sets with multivalued Euclidean projections are admitted, and the objective function may be lower semicontinuous. The particular case of convex problems is included. The obtained unconstrained or box constrained problem is solved by a version of the branch and bound method combined with local optimization. In principle, any local optimizer can be used within the branch and bound scheme but in numerical experiments sequential quadratic programming method was successfully used. So the proposed exact penalty method does not assume the existence of the objective function outside the allowable area and does not require the selection of the penalty coefficient.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10898-023-01350-4","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing its value at the projection of an infeasible point on the feasible set with the distance to the projection. Beside Euclidean projections, also a pointed projection in the direction of some fixed internal feasible point can be used. The equivalence means that local and global minimums of the problems coincide. Nonconvex sets with multivalued Euclidean projections are admitted, and the objective function may be lower semicontinuous. The particular case of convex problems is included. The obtained unconstrained or box constrained problem is solved by a version of the branch and bound method combined with local optimization. In principle, any local optimizer can be used within the branch and bound scheme but in numerical experiments sequential quadratic programming method was successfully used. So the proposed exact penalty method does not assume the existence of the objective function outside the allowable area and does not require the selection of the penalty coefficient.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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