New iterative conjugate gradient method for nonlinear unconstrained optimization

Conjugate gradient methods (CG) are an important class of methods for solving unconstrained optimization problems, especially for large-scale problems. Recently, they have been much studied. In this paper, we propose a new conjugate gradient method for unconstrained optimization. This method is a convex combination of Fletcher and Reeves (abbreviated FR), Polak–Ribiere–Polyak (abbreviated PRP) and Dai and Yuan (abbreviated DY) methods. The new conjugate gradient methods with the Wolfe line search is shown to ensure the descent property of each search direction. Some general convergence results are also established for this method. The numerical experiments are done to test the efficiency of the proposed method, which confirms its promising potentials.