Effect of Epi-convergence and Infimal Convolution Properties in Smoothing the Approximations of the Objective Function.

M. I. A. Ghitri, A. Hantoute

We use smoothing processes based on the infimal convolution of convex, proper and lower semi-continuous functions to regularize optimization problems given by means of non-convex composite functions. We show that the proposed approximations/regularization schemes still (epi-) converge to the original data, even if the chosen kernel is any convex function. This also allows for the derivation of upper estimates of the sub-differentials of the epi-limits of non-convex functions, without the use of qualifications (namely, BCQ-type conditions).

Keywords: Infimal convolution ⋅ Epi-convergence ⋅ Convex-composite function ⋅ Subdifferential ⋅ Deconvolution ⋅ Lower semi-continuous.

GT13.OPTCONT6 Invited Session
November 7, 2023  11:40 AM
CC1: Audience

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