Generalized CG-algorithms Based on Rational Sigmoid Model for Unconstrained Optimization

In this paper, we present extension forms of Dai, Yuan (DY) and Fletcher, Reveres (FR) CG algorithms. Our modifications and based on introducing a non-quadratic model (sigmoid function model). These modified algorithms are implemented with Wolfe conditions, where initial step size in each iteration is taken as and the global convergence of the modified DY algorithm is investigated. These modified algorithms are tested on some standard test functions and compared with the original DY and FR algorithms showing considerable improvements over all these comparisons.