The NC-proximal average for multiple functions

TL;DR

This paper extends the NC-proximal average to handle multiple functions, providing a generalized framework and analyzing the behavior of minimizers, which broadens its applicability in optimization problems.

Contribution

It redefines the NC-proximal average for multiple functions, expanding its theoretical foundation and offering new proofs and an example of minimizer discontinuity.

Findings

Extended the NC-proximal average to multiple functions

Provided alternative proofs using recent techniques

Analyzed discontinuity of minimizers

Abstract

The NC-proximal average is a parametrized function used to continuously transform one proper, lsc, prox-bounded function into another. Until now, it has been defined for two functions. The purpose of this article is to redefine it so that any finite number of functions may be used. The layout generally follows that of [11], extending those results to the more general case and in some instances giving alternate proofs by using techniques developed after the publication of that paper. We conclude with an example examining the discontinuity of the minimizers of the NC-proximal average.