Convex regularization and subdifferential calculus
Optimization and Control
2024-10-11 v2
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.
Cite
@article{arxiv.2410.01436,
title = {Convex regularization and subdifferential calculus},
author = {Rafael Correa and Abderrahim Hantoute and Marco A. López},
journal= {arXiv preprint arXiv:2410.01436},
year = {2024}
}