Notes on the Dai-Yuan-Yuan modified spectral gradient method

Authors:
Yunhai Xiao;Qiuyu Wang;Dong Wang
Affiliations:
Institute of Applied Mathematics, College of Mathematics and Information Science, Henan University, Kaifeng, 475004, PR China;Department of Public Computer Teaching and Research, Henan University, Kaifeng, 475004, PR China;Department of Public Computer Teaching and Research, Henan University, Kaifeng, 475004, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

In this paper, we give some notes on the two modified spectral gradient methods which were developed in [10]. 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.