非凸非光滑优化问题的两步惯性 Bregman 邻近交替线性极小化算法

Abstract

Abstract:

In this paper, for solving a class of nonconvex and nonsmooth nonseparable optimization problems, based on proximal alternating linearized minimization method we propose a new iterative algorithm which combines two-step inertial extrapolation and Bregman distance. By constructing appropriate benefit function, with the help of Kurdyka-Łojasiewicz property we establish the convergence of the whole sequence generated by proposed algorithm. We apply the proposed algorithm to solve sparse nonnegative matrix factorization, signal recovery and quadratic fractional programming problems, and show the effectiveness of proposed algorithm.

Key words: Nonconvex and nonsmooth optimization, Proximal alternating linearized minimization, Inertial extrapolation, Bregman distance, Kurdyka-Łojasiewicz property

CLC Number:

O224

Zhao Jing, Guo Chenzheng. Two-Step Inertial Bregman Proximal Alternating Linearized Minimization Algorithm for Nonconvex and Nonsmooth Problems[J].Acta mathematica scientia,Series A, 2024, 44(6): 1630-1651.

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References 40

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Two-Step Inertial Bregman Proximal Alternating Linearized Minimization Algorithm for Nonconvex and Nonsmooth Problems

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