Modifications of Hestenes and Stiefel CG Method for Solving Unconstrained Optimization Problems

Nonlinear conjugate gradient methods have a very nice theory, with a lot of important results on their convergence. This is the main argument for which these methods are intensely used in solving practical unconstrained optimization applications. There are plenty of conjugate gradient methods and can be divided to the standard conjugate gradients, hybrid and parameterized and others. This paper concerned with parameterized type conjugate gradient methods, a new search direction for nonlinear conjugate gradient algorithms is presented in this study, which is based on the Hestenes-Stefel approach and conjugacy condition, the descent property and global convergence for convex functions is proved. Numerical experiments show that the proposed algorithm is promising.