Connectedness of the approximate solution sets for set optimization problems

In this paper, we deal with connectedness of the approximate solution sets for set optimization problems by using the scalarization method. We first obtain two scalarization results for the sets of l-minimal approximate solutions and weak l-minimal approximate solutions for set optimization problems...

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Published inOptimization Vol. 71; no. 16; pp. 4819 - 4834
Main Author Han, Yu
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 16.12.2022
Taylor & Francis LLC
Subjects
approximate solution
arcwise connectedness
connectedness
Convexity
Optimization
scalarization
Set optimization problem
Set theory
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ISSN0233-1934
1029-4945
DOI10.1080/02331934.2021.1969393

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Summary:In this paper, we deal with connectedness of the approximate solution sets for set optimization problems by using the scalarization method. We first obtain two scalarization results for the sets of l-minimal approximate solutions and weak l-minimal approximate solutions for set optimization problems without using the convexity of the objective mapping and the separation theorem of convex sets. Then, we establish connectedness of the sets of l-minimal approximate solutions and weak l-minimal approximate solutions for set optimization problems by utilizing the scalarization results. Finally, we derive arcwise connectedness of the set of weak l-minimal approximate solutions for set optimization problems.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2021.1969393