Effect of Epi-convergence and Infimal Convolution Properties in Smoothing the Approximations of the Objective Function.
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).
Palabras clave: Infimal convolution ⋅ Epi-convergence ⋅ Convex-composite function ⋅ Subdifferential ⋅ Deconvolution ⋅ Lower semi-continuous.