Proximity operator characterization for abstract convex functions

Ewa Bednarczuk; The Hung Tran

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arXiv · 2606.25614

Proximity operator characterization for abstract convex functions

Ewa Bednarczuk·The Hung Tran

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Abstract

We consider proximity operator as a selector of the subgradient in the context of abstract convexity and characterize its properties in term of minimization problems. We also investigate the continuity and differentiability of proximity operator in the case of paraconvex and weakly convex functions. Supporting examples are given in each section.

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Ewa Bednarczuk, The Hung Tran. 2026-06-24. Proximity operator characterization for abstract convex functions. https://arxiv.org/abs/2606.25614

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