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

Tan Nhat Pham (), Minh N. Dao (), Andrew Eberhard () and Nargiz Sultanova ()
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Tan Nhat Pham: Federation University Australia
Minh N. Dao: RMIT University
Andrew Eberhard: RMIT University
Nargiz Sultanova: Federation University Australia

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 2, No 21, 1622-1658

Abstract: 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–Łojasiewicz 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.

Keywords: Alternating direction method of multipliers (ADMM); Bregman distance; Composite optimization problem; Difference of functions; Splitting algorithm; Linear constraints; Linearization; Multi-block structure; Nonconvex optimization; 90C26; 49M27; 65K05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02539-7

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