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arXiv · 2609.30237

Proximity operator of the weighted squared $\ell_{2,\infty}$ norm with applications

Sergio López-Rivera
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Abstract

In this paper, we derive a closed-form for the proximity operator of the weighted squared $\ell_{2,\infty}$ norm. Moreover, we derive a closed-form for the proximity operator of a weakly convex version of this function. The proof involves using known results for compute the proximity operator of a supremum function, which requires finding a solution of an auxiliary problem. We find the explicit solution of this auxiliary problem by finding the KKT multipliers and the critical point associated to the first-order optimality conditions. Additionally, we present applications to denoising problems and weighted max-min dispersion problems.

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Sergio López-Rivera. 2026-09-24. Proximity operator of the weighted squared $\ell_{2,\infty}$ norm with applications. https://arxiv.org/abs/2609.30237

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