An adaptive three-term conjugate gradient method based on self-scaling memoryless BFGS matrix

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:332

Article

Yao, Shengwei^1,2  Ning, Liangshuo¹ 

[1] Guangxi Univ Finance & Econ, Sch Informat & Stat, Nanning 530003, Peoples R China

[2] Guangxi Univ Finance & Econ, Guangxi Key Lab Cultivat Base Cross Border E Comm, Nanning 530003, Peoples R China

关键词: Unconstrained optimization;    Conjugate gradient method;    Self-scaling memoryless BFGS matrix;    Global convergence;   

DOI  :  10.1016/j.cam.2017.10.013

来源: Elsevier

【 摘 要 】

Due to its simplicity and low memory requirement, conjugate gradient methods are widely used for solving large-scale unconstrained optimization problems. In this paper, we propose a three-term conjugate gradient method. The search direction is given by a symmetrical Perry matrix, which contains a positive parameter. The value of this parameter is determined by minimizing the distance of this matrix and the self-scaling memoryless BFGS matrix in the Frobenius norm. The sufficient descent property of the generated directions holds independent of line searches. The global convergence of the given method is established under Wolfe line search for general non-convex functions. Numerical experiments show that the proposed method is promising. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free