Convergence and Stability of Line Search Methods for Unconstrained Optimization

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• 作者：Wah June Leong (1)
  Bean San Goh (2)
  
• 关键词：Line search methods ; Global convergence ; Lyapunov stability ; Globally asymptotical stability ; Unconstrained optimization ; 65K05 ; 49K40
• 刊名：Acta Applicandae Mathematicae
• 出版年：2013
• 出版时间：October 2013
• 年：2013
• 卷：127
• 期：1
• 页码：155-167
• 全文大小：483KB
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• 作者单位：Wah June Leong (1)
  Bean San Goh (2)
  
  1. Department of Mathematics, Faculty of Science, University Putra Malaysia, 43400, Serdang, Selangor, Malaysia
  2. Curtin Sarawak Research Institute, Curtin University Sarawak, 98009, Miri, Sarawak, Malaysia
  
• ISSN：1572-9036

文摘

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.