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...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
Taylor & Francis Ltd.
2012
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/40536 |
| _version_ | 1848755897963118592 |
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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. |
| first_indexed | 2025-11-14T09:03:37Z |
| format | Journal Article |
| id | curtin-20.500.11937-40536 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:03:37Z |
| publishDate | 2012 |
| publisher | Taylor & Francis Ltd. |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |