A proximal average for prox-bounded functions
Functional Analysis
2019-09-16 v1
Abstract
In this work, we construct a proximal average for two prox-bounded functions, which recovers the classical proximal average for two convex functions. The new proximal average transforms continuously in epi-topology from one proximal hull to the other. When one of the functions is differentiable, the new proximal average is differentiable. We give characterizations for Lipschitz and single-valued proximal mappings and we show that the convex combination of convexified proximal mappings is always a proximal mapping. Subdifferentiability and behaviors of infimal values and minimizers are also studied.
Cite
@article{arxiv.1909.06221,
title = {A proximal average for prox-bounded functions},
author = {Jiawei Chen and Xianfu Wang and Chayne Planiden},
journal= {arXiv preprint arXiv:1909.06221},
year = {2019}
}
Comments
45 pages including references