Two new conjugate gradient methods based on modified secant equations
Two new nonlinear conjugate gradient methods for the solution of unconstrained optimization problems are presented and evaluated. They are based on the guidelines of Dai and Liao and take into account both the gradient and function values. A modified version of the secant equation proposed by Zhang, Deng and Chen, and Zhang and Xu, characterizes the first method. The second method is based on the modified BFGS update proposed by Yuan. It is shown that one of the proposed methods is globally convergent for general functions and the other is globally convergent for uniformly convex functions, under proper conditions. For the enhancement of the performance of the line search procedure, a new approach for the computation of the initial steplength for initiating the procedure is obtained. A comparison of the proposed methods with the efficient conjugate gradient methods proposed by Dai and Liao and Hestenes and Stiefel is implemented and the numerical results demonstrate the efficiency of the two methods.
scientific article; zbMATH DE number 5710743
scientific article