A Hybrid Forward–Backward Algorithm and Its Optimization Application

Liya Liu, Xiaolong Qin and Jen-Chih Yao
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Liya Liu: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
Xiaolong Qin: Department of Mathematics, Hangzhou Normal University, Hangzhou 31121, China
Jen-Chih Yao: Research Center for Interneural Computing, China Medical University Hospital, Taichung 40447, Taiwan

Mathematics, 2020, vol. 8, issue 3, 1-16

Abstract: In this paper, we study a hybrid forward–backward algorithm for sparse reconstruction. Our algorithm involves descent, splitting and inertial ideas. Under suitable conditions on the algorithm parameters, we establish a strong convergence solution theorem in the framework of Hilbert spaces. Numerical experiments are also provided to illustrate the application in the field of signal processing.

Keywords: forward–backward method; hybrid steepest decent method; inertial extrapolation; maximally monotone; strong convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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