Compactly epi-Lipschitzian convex sets and functions in normed spaces

Borwein, Jonathan M. and Lucet, Yves and Mordukhovich, Boris S. (2000) Compactly epi-Lipschitzian convex sets and functions in normed spaces. Journal of Convex Analysis, 7 . pp. 373-394. ISSN 0944-6532

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      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.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: compactly epi-Lipschitzian set, convex set
      Subjects: UNSPECIFIED
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 25 Nov 2003
      Last Modified: 13 Jan 2015 12:26

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