Proximity Operators of Perspective Functions with Nonlinear Scaling
Optimization and Control
2024-07-08 v3
Abstract
A perspective function is a construction which combines a base function defined on a given space with a nonlinear scaling function defined on another space and which yields a lower semicontinuous convex function on the product space. Since perspective functions are typically nonsmooth, their use in first-order algorithms necessitates the computation of their proximity operator. This paper establishes closed-form expressions for the proximity operator of a perspective function defined on a Hilbert space in terms of a proximity operator involving its base function and one involving its scaling function.
Cite
@article{arxiv.2303.05337,
title = {Proximity Operators of Perspective Functions with Nonlinear Scaling},
author = {Luis M. Briceño-Arias and Patrick L. Combettes and Francisco J. Silva},
journal= {arXiv preprint arXiv:2303.05337},
year = {2024}
}