A conjugate gradient method with descent direction for unconstrained optimization

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:233

Article

Yuan, Gonglin¹  Lu, Xiwen²  Wei, Zengxin¹ 

[1] Guangxi Univ, Coll Math & Informat Sci, Nanning 530004, Guangxi, Peoples R China

[2] E China Univ Sci & Technol, Sch Sci, Shanghai 200237, Peoples R China

关键词: Search direction;    Line search;    Conjugate gradient method;    Global convergence;    Unconstrained optimization;   

DOI  :  10.1016/j.cam.2009.08.001

来源: Elsevier

【 摘 要 】

A modified conjugate gradient method is presented for solving unconstrained optimization problems, which possesses the following properties: (i) The sufficient descent property is satisfied without any line search; (ii) The search direction will be in a trust region automatically; (iii) The Zoutendijk condition holds for the Wolfe-Powell line search technique; (iv) This method inherits an important property of the well-known Polak-Ribiere-Polyak (PRP) method: the tendency to turn towards the steepest descent direction if a small step is generated away from the solution, preventing a sequence of tiny steps from happening. The global convergence and the linearly convergent rate of the given method are established. Numerical results show that this method is interesting. (C) 2009 Elsevier B.V. All rights reserved.