# Variable Metric Composite Proximal Alternating Linearized Minimization for Nonconvex Nonsmooth Optimization

arXiv: https://arxiv.org/abs/2209.06799 · HTML: https://mlsanity.com/paper/2209.06799/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2022.

## Built on by (most cited first, 1 of 1)

- [Generalized Geometry Block Proximal Linearized Method for Multiblock Nonconvex and Nonsmooth Optimization](https://mlsanity.com/paper/2609.39301/) (2026)

## Abstract (arXiv)

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.