Performance Analysis of New Spectral and Hybrid Conjugate Gradient Methods for Solving Unconstrained Optimization Problems

The spectral and hybrid conjugate gradient methods are part of the conjugate gradient methods. Conjugate gradient methods are among the iterative method for solving unconstrained optimization problems. In this paper, a new spectral and hybrid conjugate gradient methods are proposed. Based on some assumptions and strong Wolfe line search, the new spectral conjugate gradient method satisfies the global convergence properties. As well as the hybrid conjugate gradient method fulfill the global convergence properties under an exact line search. We also prove that the proposed methods fulfill the sufficient descent condition. Finally, based on some test problems, the numerical results of the proposed methods are very competitive and most efficient.