A conjugate gradient method with descent direction for unconstrained optimization

作者：Yuan, Gonglin^*; Lu, Xiwen; Wei, Zengxin

来源：Journal of Computational and Applied Mathematics, 2009, 233(2): 519-530.

DOI：10.1016/j.cam.2009.08.001

• Search direction
• Line search
• Conjugate gradient method
• Global convergence
• Unconstrained optimization

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.

• 出版日期2009-11-15
• 单位华东理工大学; 广西大学