Proximal mappings and moreau envelopes of single-variable convex piecewise cubic functions and multivariable gauge functions

Authors

Chayne Planiden, University of WollongongFollow
Xianfu Wang, University of British Columbia, OkanaganFollow

RIS ID

135279

Publication Details

Planiden, C. & Wang, X. (2019). Proximal mappings and moreau envelopes of single-variable convex piecewise cubic functions and multivariable gauge functions. In S. Hosseini, B. S. Mordukhovich & A. Uschmajew (Eds.), Nonsmooth Optimization and Its Applications (pp. 89-130). Switzerland: Springer Nature.

Abstract

This work presents a collection of useful properties of the Moreau envelope for finite-dimensional, proper, lower semicontinuous, convex functions. In particular, gauge functions and piecewise cubic functions are investigated and their Moreau envelopes categorized. Characterizations of convex Moreau envelopes are established; topics include strict convexity, strong convexity, and Lipschitz continuity.