Convergence and Stability of Line Search Methods for Unconstrained Optimization
This paper explores the stability of general line search methods in the sense of Lyapunov, for minimizing a smooth nonlinear function. In particular we give sufficient conditions for a line search method to be globally asymptotical stable. Our analysis suggests that the proposed sufficient condition...
| Main Authors: | , |
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| Format: | Journal Article |
| Published: |
Springer
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/17464 |
| _version_ | 1848749473213186048 |
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| author | Leong, Wah Goh, Bean |
| author_facet | Leong, Wah Goh, Bean |
| author_sort | Leong, Wah |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper explores the stability of general line search methods in the sense of Lyapunov, for minimizing a smooth nonlinear function. In particular we give sufficient conditions for a line search method to be globally asymptotical stable. Our analysis suggests that the proposed sufficient conditions for asymptotical stability is equivalent to the Zoutendijk-type conditions in conventional global convergence analysis. |
| first_indexed | 2025-11-14T07:21:30Z |
| format | Journal Article |
| id | curtin-20.500.11937-17464 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:21:30Z |
| publishDate | 2013 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-174642017-09-13T15:44:15Z Convergence and Stability of Line Search Methods for Unconstrained Optimization Leong, Wah Goh, Bean Line search methods Lyapunov stability Globally asymptotical stability Global convergence Unconstrained optimization This paper explores the stability of general line search methods in the sense of Lyapunov, for minimizing a smooth nonlinear function. In particular we give sufficient conditions for a line search method to be globally asymptotical stable. Our analysis suggests that the proposed sufficient conditions for asymptotical stability is equivalent to the Zoutendijk-type conditions in conventional global convergence analysis. 2013 Journal Article http://hdl.handle.net/20.500.11937/17464 10.1007/s10440-012-9796-x Springer restricted |
| spellingShingle | Line search methods Lyapunov stability Globally asymptotical stability Global convergence Unconstrained optimization Leong, Wah Goh, Bean Convergence and Stability of Line Search Methods for Unconstrained Optimization |
| title | Convergence and Stability of Line Search Methods for Unconstrained Optimization |
| title_full | Convergence and Stability of Line Search Methods for Unconstrained Optimization |
| title_fullStr | Convergence and Stability of Line Search Methods for Unconstrained Optimization |
| title_full_unstemmed | Convergence and Stability of Line Search Methods for Unconstrained Optimization |
| title_short | Convergence and Stability of Line Search Methods for Unconstrained Optimization |
| title_sort | convergence and stability of line search methods for unconstrained optimization |
| topic | Line search methods Lyapunov stability Globally asymptotical stability Global convergence Unconstrained optimization |
| url | http://hdl.handle.net/20.500.11937/17464 |