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Subspace methods for large scale nonlinear equations and nonlinear least squares
Yuan, Ya-Xiang
AbstractIn this paper, we study large scale nonlinear systems of equations and nonlinear least square problems. We present subspace methods for solving these two special optimization problems. The subspace methods have the characteristic to force the next iteration in a low dimensional subspace. The main technique is to construct subproblems in low dimensions so that the computation cost in each iteration can be reduced comparing to standard approaches. The subspace approach offers a possible way to handle large scale optimization problems which are now attracting more and more attention. Actually, quite a few known techniques can be viewed as subspace methods, such as conjugate gradient method, limited memory quasi-Newton method, projected gradient method, and null space method.
KeywordNonlinear equations Nonlinear least squares Subspace Trust region Line search
WOS Research AreaEngineering ; Operations Research & Management Science ; Mathematics
WOS SubjectEngineering, Multidisciplinary ; Operations Research & Management Science ; Mathematics, Interdisciplinary Applications
WOS IDWOS:000266497700005
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Document Type期刊论文
Corresponding AuthorYuan, Ya-Xiang
AffiliationChinese Acad Sci, State Key Lab Sci & Engn Comp, ICMSEC, AMSS, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Yuan, Ya-Xiang. Subspace methods for large scale nonlinear equations and nonlinear least squares[J]. OPTIMIZATION AND ENGINEERING,2009,10(2):207-218.
APA Yuan, Ya-Xiang.(2009).Subspace methods for large scale nonlinear equations and nonlinear least squares.OPTIMIZATION AND ENGINEERING,10(2),207-218.
MLA Yuan, Ya-Xiang."Subspace methods for large scale nonlinear equations and nonlinear least squares".OPTIMIZATION AND ENGINEERING 10.2(2009):207-218.
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