The Bregman proximal average
Optimization and Control
2022-02-25 v2
Abstract
We provide a proximal average with repect to a -coercive Legendre function. In the sense of Bregman distance, the Bregman envelope of the proximal average is a convex combination of Bregman envelopes of individual functions. The Bregman proximal mapping of the average is a convex combination of convexified proximal mappings of individual functions. Techniques from variational analysis provide the keys for the Bregman proximal average.
Cite
@article{arxiv.2108.11440,
title = {The Bregman proximal average},
author = {Xianfu Wang and Heinz H. Bauschke},
journal= {arXiv preprint arXiv:2108.11440},
year = {2022}
}