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arXiv · 1909.05795

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

Chayne Planiden·Xianfu Wang
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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.

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Chayne Planiden, Xianfu Wang. 2019-09-11. Proximal mappings and Moreau envelopes of single-variable convex piecewise cubic functions and multivariable gauge functions. https://arxiv.org/abs/1909.05795

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