AL-Rafidain Journal of Computer Sciences and Mathematics

In this paper, a modified spectral conjugate gradient method for solving unconstrained optimization problems is studied, which has sufficient descent direction and global convergence with an inexact line searches. The Fletcher-Reeves restarting criterion was employed to the standard and new versions and gave dramatic savings in the computational time. The Numerical results show that the proposed method is effective by comparing it with the FR-method.
 

A new family of  CG –algorithms for large-scale unconstrained optimization is introduced in this paper using the spectral scaling for the search directions, which is a generalization of the spectral gradient method proposed by Raydan [14].
Two modifications of the method are presented, one using Barzilai line search, and the others  take  at each iteration (where  is step- size). In both cases tested for the  Wolfe conditions, eleven test problems with different dimensions are used to compare these algorithms against the  well-known Fletcher –Revees CG-method, with obtaining a robust numerical results.