Proximal mappings and Moreau envelopes of single-variable convex piecewise cubic functions and multivariable gauge functions
Functional Analysis
2019-09-13 v1 Optimization and Control
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.
Keywords
Cite
@article{arxiv.1909.05795,
title = {Proximal mappings and Moreau envelopes of single-variable convex piecewise cubic functions and multivariable gauge functions},
author = {Chayne Planiden and Xianfu Wang},
journal= {arXiv preprint arXiv:1909.05795},
year = {2019}
}
Comments
43 pages including references, 11 figures