A New Paired Spectral Gradient Method to Improve Unconstrained and Non-Linear Optimization

The conjugated spectral gradient (SCG) method is an effective method for non-constrained large-scale nonlinear optimization. In this work, a new spectral conjugate gradient method is proposed with a strong Wolfe-Powell line search (SWP). The new proposal is based on using the formula obtained by comparing the proposed algorithm with previously published conjugate gradient algorithms. Under the usual assumptions, the descent properties and overall global convergence of the proposed method are proved. The proposed method is numerically proven to be effective.