J. Comp. Math., 33 (2015), pp. 179-190.


A Direct Search Frame-Based Adaptive Barzilai-Borwein Method

Xiaowei Fang 1, Qin Ni 2

1 College of Sciences,Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; Department of Mathematics, Huzhou University, Huzhou 313000, China
2 College of Sciences,Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received 2014-5-5 Accepted 2014-11-26
Available online 2015-3-13
doi:10.4208/jcm.1411-m4519

Abstract

This paper proposes a direct search frame-based adaptive Barzilai-Borwein method for unconstrained minimization. The method is based on the framework of frame-based algorithms proposed by Coope and Price, but we use the strategy of ABB method and the rotational minimal positive basis to reduce the computation work at each iteration. Under some mild assumptions, the convergence of this approach will be established. Through five hundreds and twenty numerical tests using the CUTEr test problem library, we show that the proposed method is promising.

Key words: Direct search, Rotational minimal positive basis, Adaptive Barzilai-Borwein method.

AMS subject classifications: 90C56, 90C30, 65K05.


Email: fangxiaowei@163.com, niqfs@nuaa.edu.cn
 

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