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arXiv · 2401.02635

Bregman Proximal Linearized ADMM for Minimizing Separable Sums Coupled by a Difference of Functions

Tan Nhat Pham·Minh N. Dao·Andrew Eberhard·Nargiz Sultanova
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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.

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Tan Nhat Pham, Minh N. Dao, Andrew Eberhard, Nargiz Sultanova. 2024-01-05. Bregman Proximal Linearized ADMM for Minimizing Separable Sums Coupled by a Difference of Functions. https://doi.org/10.1007/s10957-024-02539-7

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