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arXiv · 2410.01436

Convex regularization and subdifferential calculus

Rafael Correa·Abderrahim Hantoute·Marco A. López
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Abstract

This paper deals with the regularization of the sum of functions defined on a locally convex spaces through their closed-convex hulls in the bidual space. Different conditions guaranteeing that the closed-convex hull of the sum is the sum of the corresponding closed-convex hulls are provided. These conditions are expressed in terms of some epsilon-subdifferential calculus rules for the sum. The case of convex functions is also studied, and exact calculus rules are given under additional continuity/qualifications conditions. As an illustration, a variant of the proof of the classical Rockafellar theorem on convex integration is proposed.

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Rafael Correa, Abderrahim Hantoute, Marco A. López. 2024-10-02. Convex regularization and subdifferential calculus. https://arxiv.org/abs/2410.01436

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