Variable Metric Composite Proximal Alternating Linearized Minimization for Nonconvex Nonsmooth Optimization

Maryam Yashtini

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arXiv · 2209.06799

Variable Metric Composite Proximal Alternating Linearized Minimization for Nonconvex Nonsmooth Optimization

Maryam Yashtini

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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.

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BibTeX RIS

Maryam Yashtini. 2022-09-14. Variable Metric Composite Proximal Alternating Linearized Minimization for Nonconvex Nonsmooth Optimization. https://arxiv.org/abs/2209.06799

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