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arXiv · 1909.06221

A proximal average for prox-bounded functions

Jiawei Chen·Xianfu Wang·Chayne Planiden
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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.

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Jiawei Chen, Xianfu Wang, Chayne Planiden. 2019-09-10. A proximal average for prox-bounded functions. https://arxiv.org/abs/1909.06221

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