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

Authors :
Pham, Tan Nhat
Dao, Minh N.
Eberhard, Andrew
Sultanova, Nargiz
Source :
Journal of Optimization Theory & Applications. Nov2024, Vol. 203 Issue 2, p1622-1658. 37p.
Publication Year :
2024

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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00223239
Volume :
203
Issue :
2
Database :
Academic Search Index
Journal :
Journal of Optimization Theory & Applications
Publication Type :
Academic Journal
Accession number :
180830523
Full Text :
https://doi.org/10.1007/s10957-024-02539-7