Spectral Fletcher-Reeves Algorithm for Solving Non-Linear Unconstrained Optimization Problems

Abstract

The non-linear conjugate gradient method is a very useful technique for solving Large-Scale minimization problems and has wide applications in many fields . In this paper, we present a new spectral type, a non-linear conjugate gradient algorithm the derivatation of this algorithm is based on Fletcher – Reeves and Newton algorithm, the descent property for the suggested algorithm is proved provided that the step size satisfies the Wolfe conditions. Numerical results show that the new algorithm is efficient in practical computation and superior to the Fletcher – Reervs algorithm in many situations.