Geodesic
Compactly Epi-Lipschitzian Convex Sets and Functions in Normed Spaces
Journal of convex analysis, Tome 7 (2000) no. 2, pp. 375-394 Cet article a éte moissonné depuis la source Heldermann Verlag

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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. 
@article{JCA_2000_7_2_JCA_2000_7_2_a7,
     author = {J. Borwein and Y. Lucet and B. Mordukhovich},
     title = {Compactly {Epi-Lipschitzian} {Convex} {Sets} and {Functions} in {Normed} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {375--394},
     year = {2000},
     volume = {7},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2000_7_2_JCA_2000_7_2_a7/}
}
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J. Borwein; Y. Lucet; B. Mordukhovich. Compactly Epi-Lipschitzian Convex Sets and Functions in Normed Spaces. Journal of convex analysis, Tome 7 (2000) no. 2, pp. 375-394. http://geodesic.mathdoc.fr/item/JCA_2000_7_2_JCA_2000_7_2_a7/