PreprintCC BY 4.0arXiv
Proximity operator of the weighted squared ℓ2,∞ norm with applications
Abstract
In this paper, we derive a closed-form for the proximity operator of the weighted squared ℓ2,∞ 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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BibTeX
@misc{lopezrivera2026proximity,
title = {{Proximity operator of the weighted squared $\ell_2,\infty$ norm with applications}},
author = {Sergio López-Rivera},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30237},
eprint = {2609.30237},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30237},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Proximity operator of the weighted squared ℓ_2,∞ norm with applications
AU - Sergio López-Rivera
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30237
UR - https://arxiv.org/abs/2609.30237
AB - In this paper, we derive a closed-form for the proximity operator of the weighted squared ℓ_2,∞ 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.
ER -