Compactly epi-Lipschitzian convex sets and functions in normed spaces

Title: Compactly epi-Lipschitzian convex sets and functions in normed spaces
Creator: Borwein, Jonathan; Lucet, Yves; Mordukhovich, Boris
Relation: Journal of Convex Analysis Vol. 7, Issue 2, p. 375-393
Relation: http://www.emis.de/journals/JCA/vol.7_no.2/8.html
Publisher: Heldermann Verlag
Resource Type: journal article
Date: 2000
Description: We provide several characterizations of compact epi-Lipschitzness for closed convex sets in normed vector spaces. In particular, we show that a closed convex set is compactly epi-Lipschitzian if and only if it has nonempty relative interior, finite codimension, and spans a closed subspace. Next, we establish that all boundary points of compactly epi-Lipschitzian sets are proper support points. We provide the corresponding results for functions by using inf-convolutions and the Legendre-Fenchel transform. We also give an application to constrained optimization with compactly epi-Lipschitzian data via a generalized Slater condition involving relative interiors.
Subject: compactly epi Lipschitzian set; convex set
Identifier: http://hdl.handle.net/1959.13/940663
Identifier: uon:13062
Identifier: ISSN:0944-6532
Language: eng
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