Alternate step gradient method
Dai, YH
Source PublicationOPTIMIZATION
AbstractThe Barzilai and Borwein (BB) gradient method does not guarantee a descent in the objective function at each iteration, but performs better than the classical steepest descent (SD) method in practice. So far, the BB method has found many successful applications and generalizations in linear systems. unconstrained optimization, convex-constrained optimization, stochastic optimization, etc. In this article. we propose a new gradient method that uses the SD and the 1313 steps alternately. Hence the name "alternate step (AS) gradient method." Our theoretical and numerical analyses show that the AS method is a promising alternative to the 1313 method for linear systems. Unconstrained optimization algorithms related to the AS method are also discussed. particularly, a more efficient gradient algorithm is provided by exploring the idea of the AS method in the GBB algorithm by Raydan (1997). To establish a general R-linear convergence result for gradient methods, an important property of the stepsize is drawn in this article. Consequently, R-linear convergence result is established for a large collection of gradient methods, including the AS method. Some interesting insights into gradient methods and discussion about monotonicity and nonmonotonicity are also given.
Keywordlinear system unconstrained optimizations gradient method convergence rate nonmonotone line search
WOS Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000186897600003
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Document Type期刊论文
Corresponding AuthorDai, YH
AffiliationChinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Dai, YH. Alternate step gradient method[J]. OPTIMIZATION,2003,52(4-5):395-415.
APA Dai, YH.(2003).Alternate step gradient method.OPTIMIZATION,52(4-5),395-415.
MLA Dai, YH."Alternate step gradient method".OPTIMIZATION 52.4-5(2003):395-415.
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