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Mathematics > Optimization and Control

arXiv:1812.00604 (math)
[Submitted on 3 Dec 2018 (v1), last revised 24 Mar 2023 (this version, v5)]

Title:Quasi-Relative Interiors for Graphs of Convex Set-Valued Mappings

Authors:Dang Van Cuong, Boris S. Mordukhovich, Nguyen Mau Nam
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Abstract:This paper aims at providing further studies of the notion of quasi-relative interior for convex sets introduced by Borwein and Lewis. We obtain new formulas for representing quasi-relative interiors of convex graphs of set-valued mappings and for convex epigraphs of extended-real-valued functions defined on locally convex topological vector spaces. We also show that the role, which this notion plays in infinite dimensions and the results obtained in this vein, are similar to those involving relative interior in finite-dimensional spaces.
Comments: This submission replaces our previous versions
Subjects: Optimization and Control (math.OC)
MSC classes: 49J52, 49J53, 90C31
Cite as: arXiv:1812.00604 [math.OC]
  (or arXiv:1812.00604v5 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.1812.00604

Submission history

From: Nguyen Mau Nam [view email]
[v1] Mon, 3 Dec 2018 08:50:49 UTC (24 KB)
[v2] Tue, 11 Dec 2018 22:17:25 UTC (1 KB) (withdrawn)
[v3] Fri, 14 Dec 2018 10:33:16 UTC (18 KB)
[v4] Mon, 19 Apr 2021 03:37:03 UTC (17 KB)
[v5] Fri, 24 Mar 2023 17:02:06 UTC (17 KB)
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