A Global Convergence of Spectral Conjugate Gradient Method for Large Scale Optimization

In this paper, we are concerned with the conjugate gradient method for solving unconstrained optimization problems due to its simplicity and don’t store any matrices. We proposed two spectral modifications to the conjugate descent (CD). These two proposed methods produces sufficient descent directions for the objective function at every iteration with strong Wolfe line searches and with inexact line search, and also they are globally convergent for general non-convex functions can be guaranteed. Numerical results show the efficiency of these two proposed methods.