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Recent advances in trust region algorithms
Yuan, Ya-xiang
AbstractTrust region methods are a class of numerical methods for optimization. Unlike line search type methods where a line search is carried out in each iteration, trust region methods compute a trial step by solving a trust region subproblem where a model function is minimized within a trust region. Due to the trust region constraint, nonconvex models can be used in trust region subproblems, and trust region algorithms can be applied to nonconvex and ill-conditioned problems. Normally it is easier to establish the global convergence of a trust region algorithm than that of its line search counterpart. In the paper, we review recent results on trust region methods for unconstrained optimization, constrained optimization, nonlinear equations and nonlinear least squares, nonsmooth optimization and optimization without derivatives. Results on trust region subproblems and regularization methods are also discussed.
KeywordTrust region algorithms Nonlinear optimization Subproblem Complexity Convergence
Funding ProjectNational Natural Science Foundation of China[11331012] ; National Natural Science Foundation of China[11321061] ; National Natural Science Foundation of China[11461161005]
WOS Research AreaComputer Science ; Operations Research & Management Science ; Mathematics
WOS SubjectComputer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000354623300010
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Document Type期刊论文
Corresponding AuthorYuan, Ya-xiang
AffiliationChinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Yuan, Ya-xiang. Recent advances in trust region algorithms[J]. MATHEMATICAL PROGRAMMING,2015,151(1):249-281.
APA Yuan, Ya-xiang.(2015).Recent advances in trust region algorithms.MATHEMATICAL PROGRAMMING,151(1),249-281.
MLA Yuan, Ya-xiang."Recent advances in trust region algorithms".MATHEMATICAL PROGRAMMING 151.1(2015):249-281.
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