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arXiv · 2108.11440

The Bregman proximal average

Xianfu Wang·Heinz H. Bauschke
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Abstract

We provide a proximal average with repect to a $1$-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.

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Xianfu Wang, Heinz H. Bauschke. 2021-08-25. The Bregman proximal average. https://arxiv.org/abs/2108.11440

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