Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: López-Rivera, Sergio
Institution: Universidad Técnica Federico Santa María
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214351775