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Open AccessArticle

A Hybrid Forward–Backward Algorithm and Its Optimization Application

1
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
2
Department of Mathematics, Hangzhou Normal University, Hangzhou 31121, China
3
Research Center for Interneural Computing, China Medical University Hospital, Taichung 40447, Taiwan
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 447; https://doi.org/10.3390/math8030447 (registering DOI)
Received: 25 February 2020 / Revised: 17 March 2020 / Accepted: 18 March 2020 / Published: 19 March 2020
(This article belongs to the Special Issue Nonlinear Analysis and Optimization)
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. View Full-Text
Keywords: forward–backward method; hybrid steepest decent method; inertial extrapolation; maximally monotone; strong convergence forward–backward method; hybrid steepest decent method; inertial extrapolation; maximally monotone; strong convergence
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Liu, L.; Qin, X.; Yao, J.-C. A Hybrid Forward–Backward Algorithm and Its Optimization Application. Mathematics 2020, 8, 447.

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