Derivative-Free Three-Term Spectral Conjugate Gradient Method for Symmetric Nonlinear Equations

In this paper, we proposed a new derivative-free three-term spectral conjugate gradient (DFTTS) method via extending the direction proposed by Birgin and Mertinez [E.G. Birgin, J.M. Martinez, A spectral Conjugate Gradient Method for Unconstrained Optimization, Appl. Math. Optim. 43 (2) (2001) 117--128] to three-term together with the classical Newton's direction. One of the important properties of the proposed method is that, it generated a descent direction using inexact line search. The global convergence of the proposed algorithm was established under appropriate conditions. Numerical results for the benchmark test problems demonstrated an improved efficiency of the method over some existing ones.