A Modified PRP Formula For Unconstrained Optimization Problems

The conjugate gradient method is one of the most efficient methods for solving unconstrained optimization problems. In this thesis, a modified Polak-Ribiere-Polyak conjugate gradient formula was proposed for unconstrained optimization. This formula with non-negative values possesses some favorable properties: (1) the sufficient descent condition holds without any line searches; (2) conjugate gradient methods with this formula and some certain steplength technique which ensures the Zoutendijk condition to be held are globally convergent. In addition, a global convergent conjugate gradient-type algorithm with the standard Arrnijo line search is also presented. Preliminary numerical results show that the proposed method with weak Wolfe line search is very promising.