An efficient spectral conjugate gradient parameter with descent condition for unconstrained optimization

The spectral gradient parameters and conjugate gradient algorithms are among the most efficient algorithms for solving large-scale unconstrained optimization problems. This is due to efficient numerical performance and simplicity of their algorithms. Numerous studies have been done recently to improve these methods. In this paper, we proposed an efficient spectral conjugate gradient algorithm by combining the spectral gradient parameter and conjugate gradient coefficient. The modified spectral conjugate gradient method satisfies the sufficient descent condition independent of line search procedure. An interesting feature of the proposed method is that it can be applied to large-scale unconstrained optimization problems. Preliminary numerical results are presented under strong Wolfe line search to illustrate the efficiency of the proposed method.