Abstract

       In this paper, we have proposed a new family of four and five- parameters conjugate gradient methods for solving nonlinear unconstrained optimization problems. They are depend on at most five parameters and include the already-existing ten practical nonlinear conjugate gradient methods. They are subsumes some other families of nonlinear conjugate gradient methods as its subfamilies, with Powell’s restart criterion. The new proposed family with strong Wolfe-Powell line searches are ensure the descent property for each search direction. Some general convergence results are established for the proposed family. Our numerical results are very promising in general by using several nonlinear test functions.

Key words: Unconstrained Optimization, Conjugate Gradient methods, Exact Lines Search, Global Convergence property.