Geodesic
Remarks on the Γ--regularization of Non-convex and Non-semi-continuous Functions on Topological Vector Spaces
Journal of convex analysis, Tome 19 (2012) no. 2, pp. 467-483

Voir la notice de l'article provenant de la source Heldermann Verlag

We show that the minimization problem of any non-convex and non-lower semi-continuous function on a compact convex subset of a locally convex real topological vector space can be studied via an associated convex and lower semi-continuous function Γ(h). This observation uses the notion of Γ-regularization as a key ingredient. As an application we obtain, on any locally convex real space, a generalization of the Lanford III--Robinson theorem which has only been proven for separable real Banach spaces. The latter is a characterization of subdifferentials of convex continuous functions.
Classification : 58E30, 46N10, 52A07
Mots-clés : Variational problems, non-linear analysis, non-convexity, Gamma-regularization, Lanford III -- Robinson theorem 
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     author = {J.-B. Bru and W. de Siqueira Pedra},
     title = {Remarks on the {\ensuremath{\Gamma}--regularization} of {Non-convex} and {Non-semi-continuous} {Functions} on {Topological} {Vector} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {467--483},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2012},
     url = {http://geodesic.mathdoc.fr/item/JCA_2012_19_2_JCA_2012_19_2_a7/}
}
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J.-B. Bru; W. de Siqueira Pedra. Remarks on the Γ--regularization of Non-convex and Non-semi-continuous Functions on Topological Vector Spaces. Journal of convex analysis, Tome 19 (2012) no. 2, pp. 467-483. http://geodesic.mathdoc.fr/item/JCA_2012_19_2_JCA_2012_19_2_a7/