A new family of conjugate gradient methods

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:224

Article

Shi, Zhen-Jun^1,2  Guo, Jinhua¹ 

[1] Univ Michigan, Dept Comp & Informat Sci, Dearborn, MI 48128 USA

[2] Qufu Normal Univ, Coll Operat Res & Management, Rizhao 276826, Shandong, Peoples R China

关键词: Unconstrained optimization;    Conjugate gradient method;    Global convergence;   

DOI  :  10.1016/j.cam.2008.05.012

来源: Elsevier

【 摘 要 】

In this paper we develop a new class of conjugate gradient methods for unconstrained optimization problems. A new nonmonotone line search technique is proposed to guarantee the global convergence of these conjugate gradient methods under some mild conditions. In particular, Polak-Ribiere-Polyak and Liu-Storey conjugate gradient methods are special cases of the new class of conjugate gradient methods. By estimating the local Lipschitz constant of the derivative of objective functions, we can find an adequate step size and substantially decrease the function evaluations at each iteration. Numerical results show that these new conjugate gradient methods are effective in minimizing large-scale non-convex non-quadratic functions. (c) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free