A Hybrid Forward–Backward Algorithm and Its Optimization Application

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....

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Main Authors:	Liya Liu, Xiaolong Qin, Jen-Chih Yao
Format:	Article
Language:	English
Published:	MDPI AG 2020-03-01
Series:	Mathematics
Subjects:	forward–backward method hybrid steepest decent method inertial extrapolation maximally monotone strong convergence
Online Access:	https://www.mdpi.com/2227-7390/8/3/447

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spelling	doaj-6a4607bd2b2d4aeea60ed5af6705216f2020-11-25T03:35:27ZengMDPI AGMathematics2227-73902020-03-018344710.3390/math8030447math8030447A Hybrid Forward–Backward Algorithm and Its Optimization ApplicationLiya Liu0Xiaolong Qin1Jen-Chih Yao2School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, ChinaDepartment of Mathematics, Hangzhou Normal University, Hangzhou 31121, ChinaResearch Center for Interneural Computing, China Medical University Hospital, Taichung 40447, TaiwanIn 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.https://www.mdpi.com/2227-7390/8/3/447forward–backward methodhybrid steepest decent methodinertial extrapolationmaximally monotonestrong convergence
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Liya Liu Xiaolong Qin Jen-Chih Yao
spellingShingle	Liya Liu Xiaolong Qin Jen-Chih Yao A Hybrid Forward–Backward Algorithm and Its Optimization Application Mathematics forward–backward method hybrid steepest decent method inertial extrapolation maximally monotone strong convergence
author_facet	Liya Liu Xiaolong Qin Jen-Chih Yao
author_sort	Liya Liu
title	A Hybrid Forward–Backward Algorithm and Its Optimization Application
title_short	A Hybrid Forward–Backward Algorithm and Its Optimization Application
title_full	A Hybrid Forward–Backward Algorithm and Its Optimization Application
title_fullStr	A Hybrid Forward–Backward Algorithm and Its Optimization Application
title_full_unstemmed	A Hybrid Forward–Backward Algorithm and Its Optimization Application
title_sort	hybrid forward–backward algorithm and its optimization application
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2020-03-01
description	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.
topic	forward–backward method hybrid steepest decent method inertial extrapolation maximally monotone strong convergence
url	https://www.mdpi.com/2227-7390/8/3/447
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A Hybrid Forward–Backward Algorithm and Its Optimization Application

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