Investigation on Extended Conjugate Gradient Non-linear methods for solving Unconstrained Optimization

Abstract In this paper we have generalized the extended Dai-Yuan conjugate Gradient method by Considering the parameter in the denominator of as a convex combination. Three values of are computed in three different ways namely by assuming descent property, Pure Conjugacy and using Newton direction. The descent property and global convergence for the proposed algorithms are established. Our numerical experiments on some standard test functions show that there are considerable improvement on other classical methods in this field.