A nonmonotone inexact Newton method for unconstrained optimization
Gao, Huan1; Zhang, Hai-Bin1; Li, Zhi-Bao2; Tadjouddine, Emmanuel3
AbstractIt is well known that the Newton method has a second order rate of convergence and that it is widely used to solve optimization problems and nonlinear equations which arise from computational science, engineering analysis and other applications. However, two big disadvantages hinder its application: high computational cost for large scale problems and poor global performance in some complicated and difficult problems. Some inexact Newton methods have emerged over time. Among them, the Newton preconditioned conjugate gradient method is the most efficient and popular approach to overcome the first shortcoming while keeping rapid convergence. In this paper, we have improved the global performance of the inexact Newton method by developing a nonmonotone line search technique. We have also proved the global convergence of the proposed method under some conditions. Numerical experiments on a set of standard test problems are reported. They have shown that the proposed algorithm is promising.
KeywordInexact Newton method Nonmonotone line search Preconditioned conjugate gradient Global convergence
Funding ProjectNational Natural Science Foundation of China[61179033] ; Collaborative Innovation Center on Beijing Society-building and Social Governance ; China Postdoctoral Science Foundation[2014M561081]
WOS Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000401258300005
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Document Type期刊论文
Corresponding AuthorGao, Huan
Affiliation1.Beijing Univ Technol, Coll Appl Sci, Beijing, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing, Peoples R China
3.Xian Jiaotong Liverpool Univ, Comp Sci & Software Engn, SIP, Suzhou, Peoples R China
Recommended Citation
GB/T 7714
Gao, Huan,Zhang, Hai-Bin,Li, Zhi-Bao,et al. A nonmonotone inexact Newton method for unconstrained optimization[J]. OPTIMIZATION LETTERS,2017,11(5):947-965.
APA Gao, Huan,Zhang, Hai-Bin,Li, Zhi-Bao,&Tadjouddine, Emmanuel.(2017).A nonmonotone inexact Newton method for unconstrained optimization.OPTIMIZATION LETTERS,11(5),947-965.
MLA Gao, Huan,et al."A nonmonotone inexact Newton method for unconstrained optimization".OPTIMIZATION LETTERS 11.5(2017):947-965.
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