New BFGS method for unconstrained optimization problem based on modified Armijo line search

In this article, a class of nonconvex unconstrained optimization problems is considered. As the Armijo line search is less costing in finding a steplength, a new Armijo-type line search (called WALS) with desirable features of the Wolfe condition is employed in the proposed modified BFGS method. A n...

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Main Authors: Wan, Zhong, Teo, Kok Lay, Shen, Xianlong, Hu, Chaoming
Format: Journal Article
Published: Taylor & Francis Ltd. 2012
Subjects:
Online Access:http://hdl.handle.net/20.500.11937/40536
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author Wan, Zhong
Teo, Kok Lay
Shen, Xianlong
Hu, Chaoming
author_facet Wan, Zhong
Teo, Kok Lay
Shen, Xianlong
Hu, Chaoming
author_sort Wan, Zhong
building Curtin Institutional Repository
collection Online Access
description In this article, a class of nonconvex unconstrained optimization problems is considered. As the Armijo line search is less costing in finding a steplength, a new Armijo-type line search (called WALS) with desirable features of the Wolfe condition is employed in the proposed modified BFGS method. A new updating formula incorporated with WALS is constructed and generates approximate Hessian matrices which are positive definite. On this basis, a class of well-defined modified BFGS algorithms is developed. It shows that under some suitable conditions, the modified BFGS algorithm is globally convergent. Numerical experiments are carried out on 20 benchmark test problems and the obtained results clearly indicate the effectiveness of the developed algorithm over two most popular BFGS-type algorithms available in the literature.
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institution Curtin University Malaysia
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publishDate 2012
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spelling curtin-20.500.11937-405362017-09-13T15:58:59Z New BFGS method for unconstrained optimization problem based on modified Armijo line search Wan, Zhong Teo, Kok Lay Shen, Xianlong Hu, Chaoming global convergence Armijo-type line search unconstrained optimization BFGS method In this article, a class of nonconvex unconstrained optimization problems is considered. As the Armijo line search is less costing in finding a steplength, a new Armijo-type line search (called WALS) with desirable features of the Wolfe condition is employed in the proposed modified BFGS method. A new updating formula incorporated with WALS is constructed and generates approximate Hessian matrices which are positive definite. On this basis, a class of well-defined modified BFGS algorithms is developed. It shows that under some suitable conditions, the modified BFGS algorithm is globally convergent. Numerical experiments are carried out on 20 benchmark test problems and the obtained results clearly indicate the effectiveness of the developed algorithm over two most popular BFGS-type algorithms available in the literature. 2012 Journal Article http://hdl.handle.net/20.500.11937/40536 10.1080/02331934.2011.644284 Taylor & Francis Ltd. restricted
spellingShingle global convergence
Armijo-type line search
unconstrained optimization
BFGS method
Wan, Zhong
Teo, Kok Lay
Shen, Xianlong
Hu, Chaoming
New BFGS method for unconstrained optimization problem based on modified Armijo line search
title New BFGS method for unconstrained optimization problem based on modified Armijo line search
title_full New BFGS method for unconstrained optimization problem based on modified Armijo line search
title_fullStr New BFGS method for unconstrained optimization problem based on modified Armijo line search
title_full_unstemmed New BFGS method for unconstrained optimization problem based on modified Armijo line search
title_short New BFGS method for unconstrained optimization problem based on modified Armijo line search
title_sort new bfgs method for unconstrained optimization problem based on modified armijo line search
topic global convergence
Armijo-type line search
unconstrained optimization
BFGS method
url http://hdl.handle.net/20.500.11937/40536