Variable Metric Composite Proximal Alternating Linearized Minimization for Nonconvex Nonsmooth Optimization
Abstract
In this paper we propose a proximal algorithm for minimizing an objective function of two block variables consisting of three terms: 1) a smooth function, 2) a nonsmooth function which is a composition between a strictly increasing, concave, differentiable function and a convex nonsmooth function, and 3) a smooth function which couples the two block variables. We propose a variable metric composite proximal alternating linearized minimization (CPALM) to solve this class of problems. Building on the powerful Kurdyka-\L ojasiewicz property, we derive the convergence analysis and establish that each bounded sequence generated by CPALM globally converges to a critical point. We demonstrate the CPALM method on parallel magnetic resonance image reconstruction problems. The obtained numerical results shows the viability and effectiveness of the proposed method.
Cite
@article{arxiv.2209.06799,
title = {Variable Metric Composite Proximal Alternating Linearized Minimization for Nonconvex Nonsmooth Optimization},
author = {Maryam Yashtini},
journal= {arXiv preprint arXiv:2209.06799},
year = {2022}
}