A New Modification of Fletcher-Reeves Conjugate Gradient Method for Unconstrained Optimization Models

Abstract

The Conjugate Gradient (CG) algorithm is among the prominent iterative scheme employed for obtaining the solution of sparse systems of linear equations. These methods are widely used in many fields because of their nice convergence properties and the requirements of low memory. In this paper, we introduced the idea of quadratic forms and used it to derive the Conjugate Directions, an important property used in the convergence analysis of CG method, and further extend it to construct an efficient modification of FR CG algorithm. The proposed method possesses the sufficient descent property and the global convergence was established under the inexact line search. Preliminary results have been presented which show that the new algorithm is effective and promising when compared to some existing CG methods.