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

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 fu...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 203; no. 2; pp. 1622 - 1658
Main Authors: Pham, Tan Nhat, Dao, Minh N., Eberhard, Andrew, Sultanova, Nargiz
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2024
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
Composite optimization problem
Nonconvex optimization
65K05
Multi-block structure
Difference of functions
Linear constraints
Splitting algorithm
90C26
49M27
Bregman distance
Alternating direction method of multipliers (ADMM)
Linearization
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary: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.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-024-02539-7