Epiconvergence, the Moreau envelope and generalized linear-quadratic functions
Functional Analysis
2019-09-12 v1
Abstract
This work introduces the class of generalized linear-quadratic functions, constructed using maximally monotone symmetric linear relations. Calculus rules and properties of the Moreau envelope for this class of functions are developed. In finite dimensions, on a metric space defined by Moreau envelopes, we consider the epigraphical limit of a sequence of quadratic functions and categorize the results. We explore the question of when a quadratic function is a Moreau envelope of a generalized linear-quadratic function; characterizations involving nonexpansiveness and Lipschitz continuity are established. This work generalizes some results by Hiriart-Urruty and by Rockafellar and Wets.
Cite
@article{arxiv.1909.04848,
title = {Epiconvergence, the Moreau envelope and generalized linear-quadratic functions},
author = {Chayne Planiden and Xianfu Wang},
journal= {arXiv preprint arXiv:1909.04848},
year = {2019}
}
Comments
42 pages including references, 5 figures