Global Convergence Condition for a New Spectral Conjugate Gradient Method for Large-Scale Optimization

The spectral conjugate gradient (SCG) method is an effective method to solve large-scale nonlinear unconstrained optimization problems. In this work, a new spectral conjugate gradient method is proposed with a strong Wolfe-Powell line search (SWP). The idea of the new one is using the β^BZA formula which is proposed by Baluch and et al., with suitable parameter φ denoted by (SCGBZA). Under the usual assumptions, the descent properties and overall global convergence of the proposed method (SCGBZA) are proved. The proposed method is numerically proven to be effective.