A class of spectral conjugate gradient method with descent condition for unconstrained optimization

The Spectral conjugate gradient (SCG) methods are among the most efficient conjugate gradient (CG) methods for unconstrained optimization. This is due to their low memory requirement and nice convergence properties. The success of the of SCG methods depends on effective choices of the search direction dk and the step size αk. In this paper, we present a new class of spectral conjugate gradient coefficient that possesses the sufficient descent condition. The global convergence result for general functions is established under strong Wolfe line search. Further, numerical result has been presented which shows that the methods are efficient and promising.