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Notes on the Dai-Yuan-Yuan modified spectral gradient method. (English) Zbl 1195.65081

Summary: We give some notes on the two modified spectral gradient methods which were developed by Y. Dai, J. Yuan and Y.-X. Jinyun [Comput. Optim. Appl. 22, No. 1, 103–109 (2002; Zbl 1008.90056)]. These notes present the relationship between their stepsize formulae and some new secant equations in the quasi-Newton method. In particular, we also introduce another two new choices of stepsize. By using an efficient nonmonotone line search technique, we propose some new spectral gradient methods. Under some mild conditions, we show that these proposed methods are globally convergent. Numerical experiments on a large number of test problems from the CUTEr library are also reported, which show that the efficiency of these proposed methods.

MSC:

65K05 Numerical mathematical programming methods
90C26 Nonconvex programming, global optimization
90C53 Methods of quasi-Newton type

Citations:

Zbl 1008.90056

Software:

CUTEr
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Full Text: DOI

References:

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