Generalized Relative Interiors and Generalized Convexity in Infinite-Dimensional Spaces
Sponsor
Research of Vo Si Trong Long is funded by University of Science, VNU-HCM, under grant number T2023-97. Research of Boris S. Mordukhovich was partly supported by the USA National Science Foundation under grants DMS-1808978 and DMS-2204519, by the Australian Research Council under grantDP-190100555, and by Project 111 of China under grant D21024. Research of Nguyen Mau Nam was partly supported by the USA National Science Foundation under grant DMS-2136228.
Published In
Optimization
Document Type
Citation
Publication Date
5-21-2024
Abstract
This paper focuses on investigating generalized relative interior notions for sets in locally convex topological vector spaces with particular attentions to graphs of set-valued mappings and epigraphs of extended-real-valued functions. We introduce, study, and utilize a novel notion of quasi-near convexity of sets that is an infinite-dimensional extension of the widely acknowledged notion of near convexity. Quasi-near convexity is associated with the quasi-relative interior of sets, which is investigated in the paper together with other generalized relative interior notions for sets, not necessarily convex. In this way, we obtain new results on generalized relative interiors for graphs of set-valued mappings in convexity and generalized convexity settings.
Rights
Copyright © 2024Informa UK Limited
Locate the Document
DOI
10.1080/02331934.2024.2356205
Persistent Identifier
https://archives.pdx.edu/ds/psu/42039
Citation Details
Long, V. S. T., Mordukhovich, B. S., & Nam, N. M. (2024). Generalized relative interiors and generalized convexity in infinite-dimensional spaces. Optimization, 1–31.