A conjugate gradient method with descent direction for unconstrained optimization

Authors:
Gonglin Yuan;Xiwen Lu;Zengxin Wei
Affiliations:
College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, PR China;School of Science, East China University of Science and Technology, Shanghai, 200237, PR China;College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

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.