Properties of generalized polyhedral convex multifunctions

This paper presents a study of generalized polyhedral convexity under basic operations on multifunctions. We address the preservation of generalized polyhedral convexity under sums and compositions of multifunctions, the domains and ranges of generalized polyhedral convex multifunctions, and the dir...

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Published inOptimization Vol. 74; no. 8; pp. 1763 - 1791
Main Authors Luan, Nguyen Ngoc, Nam, Nguyen Mau, Yen, Nguyen Dong
Format Journal Article
LanguageEnglish
Published Taylor & Francis 11.06.2025
Subjects
generalized interior
generalized polyhedral convex multifunction
generalized polyhedral convex set
Locally convex Hausdorff topological vector space
optimal value function
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Abstract This paper presents a study of generalized polyhedral convexity under basic operations on multifunctions. We address the preservation of generalized polyhedral convexity under sums and compositions of multifunctions, the domains and ranges of generalized polyhedral convex multifunctions, and the direct and inverse images of sets under such mappings. Then we explore the class of optimal value functions defined by a generalized polyhedral convex objective function and a generalized polyhedral convex constrained mapping. The new results provide a framework for representing the relative interior of the graph of a generalized polyhedral convex multifunction in terms of the relative interiors of its domain and mapping values in locally convex topological vector spaces. Among the new results in this paper is a significant extension of a result by Bonnans and Shapiro on the domain of generalized polyhedral convex multifunctions from Banach spaces to locally convex topological vector spaces.
AbstractList This paper presents a study of generalized polyhedral convexity under basic operations on multifunctions. We address the preservation of generalized polyhedral convexity under sums and compositions of multifunctions, the domains and ranges of generalized polyhedral convex multifunctions, and the direct and inverse images of sets under such mappings. Then we explore the class of optimal value functions defined by a generalized polyhedral convex objective function and a generalized polyhedral convex constrained mapping. The new results provide a framework for representing the relative interior of the graph of a generalized polyhedral convex multifunction in terms of the relative interiors of its domain and mapping values in locally convex topological vector spaces. Among the new results in this paper is a significant extension of a result by Bonnans and Shapiro on the domain of generalized polyhedral convex multifunctions from Banach spaces to locally convex topological vector spaces.
Author Luan, Nguyen Ngoc
Nam, Nguyen Mau
Yen, Nguyen Dong
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Snippet This paper presents a study of generalized polyhedral convexity under basic operations on multifunctions. We address the preservation of generalized polyhedral...
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StartPage 1763
SubjectTerms generalized interior
generalized polyhedral convex multifunction
generalized polyhedral convex set
Locally convex Hausdorff topological vector space
optimal value function
Title Properties of generalized polyhedral convex multifunctions
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