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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Bibliographic Details
Published in:	Optimization Vol. 74; no. 8; pp. 1763 - 1791
Main Authors:	Luan, Nguyen Ngoc, Nam, Nguyen Mau, Yen, Nguyen Dong
Format:	Journal Article
Language:	English
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
ISSN:	0233-1934, 1029-4945
Online Access:	Get full text
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Summary:	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.
ISSN:	0233-1934 1029-4945
DOI:	10.1080/02331934.2024.2420679