The Barzilai and Borwein gradient method with nonmonotone line search for nonsmooth convex optimization problems

The Barzilai and Borwein gradient method with nonmonotone line search for nonsmooth convex optimization problems

The Barzilai and Borwein gradient algorithm has received a great deal of attention in recent decades since it is simple and effective for smooth optimization problems. Whether can it be extended to solve nonsmooth problems? In this paper, we answer this question positively. The Barzilai and Borwein...

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Main Authors: Gonglin Yuan, Zengxin Wei
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2012-04-01
Series:Mathematical Modelling and Analysis
Subjects:
nonsmooth convex minimization
spectral gradient
nonmonotone technique
global convergence
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/4854
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spelling doaj-03e63c3e366a4bc9aebf5a6b7bf8eb922021-07-02T10:07:41ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102012-04-0117210.3846/13926292.2012.661375The Barzilai and Borwein gradient method with nonmonotone line search for nonsmooth convex optimization problemsGonglin Yuan0Zengxin Wei1Guangxi University 530004 Nanning, Guangxi, ChinaGuangxi University 530004 Nanning, Guangxi, China The Barzilai and Borwein gradient algorithm has received a great deal of attention in recent decades since it is simple and effective for smooth optimization problems. Whether can it be extended to solve nonsmooth problems? In this paper, we answer this question positively. The Barzilai and Borwein gradient algorithm combined with a nonmonotone line search technique is proposed for nonsmooth convex minimization. The global convergence of the given algorithm is established under suitable conditions. Numerical results show that this method is efficient. https://journals.vgtu.lt/index.php/MMA/article/view/4854nonsmooth convex minimizationspectral gradientnonmonotone techniqueglobal convergence
collection DOAJ
language English
format Article
sources DOAJ
author Gonglin Yuan
Zengxin Wei
spellingShingle Gonglin Yuan
Zengxin Wei
The Barzilai and Borwein gradient method with nonmonotone line search for nonsmooth convex optimization problems
Mathematical Modelling and Analysis
nonsmooth convex minimization
spectral gradient
nonmonotone technique
global convergence
author_facet Gonglin Yuan
Zengxin Wei
author_sort Gonglin Yuan
title The Barzilai and Borwein gradient method with nonmonotone line search for nonsmooth convex optimization problems
title_short The Barzilai and Borwein gradient method with nonmonotone line search for nonsmooth convex optimization problems
title_full The Barzilai and Borwein gradient method with nonmonotone line search for nonsmooth convex optimization problems
title_fullStr The Barzilai and Borwein gradient method with nonmonotone line search for nonsmooth convex optimization problems
title_full_unstemmed The Barzilai and Borwein gradient method with nonmonotone line search for nonsmooth convex optimization problems
title_sort barzilai and borwein gradient method with nonmonotone line search for nonsmooth convex optimization problems
publisher Vilnius Gediminas Technical University
series Mathematical Modelling and Analysis
issn 1392-6292
1648-3510
publishDate 2012-04-01
description The Barzilai and Borwein gradient algorithm has received a great deal of attention in recent decades since it is simple and effective for smooth optimization problems. Whether can it be extended to solve nonsmooth problems? In this paper, we answer this question positively. The Barzilai and Borwein gradient algorithm combined with a nonmonotone line search technique is proposed for nonsmooth convex minimization. The global convergence of the given algorithm is established under suitable conditions. Numerical results show that this method is efficient.
topic nonsmooth convex minimization
spectral gradient
nonmonotone technique
global convergence
url https://journals.vgtu.lt/index.php/MMA/article/view/4854
work_keys_str_mv AT gonglinyuan thebarzilaiandborweingradientmethodwithnonmonotonelinesearchfornonsmoothconvexoptimizationproblems
AT zengxinwei thebarzilaiandborweingradientmethodwithnonmonotonelinesearchfornonsmoothconvexoptimizationproblems
AT gonglinyuan barzilaiandborweingradientmethodwithnonmonotonelinesearchfornonsmoothconvexoptimizationproblems
AT zengxinwei barzilaiandborweingradientmethodwithnonmonotonelinesearchfornonsmoothconvexoptimizationproblems
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