A class of novel three-block Bregman-type Peaceman–Rachford splitting methods with linear approximation for solving sparse signal reconstruction problems
Fixed Point Methods and Optimization, Volume 2, Issue 2, August 2025, Pages 127–148
YING ZHAO
College of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong, 643000, Sichuan, PR China
Chengdu Qingbaijiang Experimental Primary School, Chengdu, 610300, Sichuan, PR China
HENG-YOU LAN
College of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong, 643000, Sichuan, PR China
Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing, Zigong, 643000, Sichuan, PR China
Abstract
Exploring three-block nonconvex optimization with a nonseparable structure has substantial theoretical significance and potential applications in nonconvex background or foreground extraction problems such as image and signal processing, phase retrieval, and so on. A class of novel generalized three-block Bregman-type Peaceman-Rachford splitting methods are proposed, which integrates the inexact concepts of linear approximation. Under some generalization assumptions, the optimality condition is used to establish global convergence. Furthermore, via constituting Cauchy sequence, strong convergence is proved when the augmented Lagrangian function for the three-block nonconvex and nonseparable optimizations satisfies Kurdyka-Łojasiewicz property. Lastly, a preliminary numerical application experiment associated with sparse signal reconstruction confirms the effectiveness.
Cite this Article as
Ying Zhao and Heng-Youlan, A class of novel three-block Bregman-type Peaceman–Rachford splitting methods with linear approximation for solving sparse signal reconstruction problems, Fixed Point Methods and Optimization, 2(2), 127–148, 2025