A Modified Spectral Conjugate Gradient Method with Global Convergence

In this paper, a modified version of the spectral conjugate gradient algorithm suggested by Jian, Chen, Jiang, Zeng and Yin is proposed. It is proved that the new method is globally convergent for general nonlinear functions, under some standard assumptions. Based on the modified secant condition and quasi-Newton directions, some new spectral parameters are introduced. It is shown that the search direction satisfies the sufficient descent property independent of the line search. Numerical experiments indicate a promising behavior of the new algorithm, especially for large-scale problems.