New merit functions for multiobjective optimization and their properties

A merit (gap) function is a map that returns zero at the solutions of problems and strictly positive values otherwise. Its minimization is equivalent to the original problem by definition, and it can estimate the distance between a given point and the solution set. Ideally, this function should have...

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Published inOptimization Vol. 73; no. 13; pp. 3821 - 3858
Main Authors Tanabe, Hiroki, Fukuda, Ellen H., Yamashita, Nobuo
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 03.12.2024
Taylor & Francis LLC
Subjects
composite optimization
error bounds
merit functions
Multiobjective optimization
Multiple objective analysis
Optimization
Pareto stationarity
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Summary:A merit (gap) function is a map that returns zero at the solutions of problems and strictly positive values otherwise. Its minimization is equivalent to the original problem by definition, and it can estimate the distance between a given point and the solution set. Ideally, this function should have some properties, including the ease of computation, continuity, differentiability, boundedness of the level set, and error boundedness. In this work, we propose new merit functions for multiobjective optimization with lower semicontinuous objectives, convex objectives, and composite objectives, and we show that they have such desirable properties under reasonable assumptions.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2023.2232794