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arXiv · 1610.03411

Remarks on the $\Gamma $-regularization of Non-convex and Non-semi-continuous Functions on Topological Vector Spaces

J. -B. Bru·W. de Siqueira Pedra
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Abstract

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 $\Gamma \left( h\right) $. This observation uses the notion of $\Gamma $-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.

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J. -B. Bru, W. de Siqueira Pedra. 2016-10-10. Remarks on the $\Gamma $-regularization of Non-convex and Non-semi-continuous Functions on Topological Vector Spaces. https://arxiv.org/abs/1610.03411

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