Bregman Proximal Linearized ADMM for Minimizing Separable Sums Coupled by a Difference of Functions
Abstract
In this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth functions and a smooth function, coupled by a difference of functions. This structure encapsulates numerous significant nonconvex and nonsmooth optimization problems in the current literature including the linearly constrained difference-of-convex problems. Relying on the successive linearization and alternating direction method of multipliers (ADMM), the proposed algorithm exhibits the global subsequential convergence to a stationary point of the underlying problem. We also establish the convergence of the full sequence generated by our algorithm under the Kurdyka--Lojasiewicz property and some mild assumptions. The efficiency of the proposed algorithm is tested on a robust principal component analysis problem and a nonconvex optimal power flow problem.
Cite
@article{arxiv.2401.02635,
title = {Bregman Proximal Linearized ADMM for Minimizing Separable Sums Coupled by a Difference of Functions},
author = {Tan Nhat Pham and Minh N. Dao and Andrew Eberhard and Nargiz Sultanova},
journal= {arXiv preprint arXiv:2401.02635},
year = {2024}
}