A positive spectral gradient-like method for large-scale nonlinear monotone equations

Abstract

In this work, we proposed a combine form of a positive spectral gradient-like method and projection method for solving nonlinear monotone equations. The spectral gradient-like coefficient is obtained using a convex combination of two different positive spectral coefficients. Under the monotonicity and Lipschitz continuity assumptions, the method is shown to be globally convergent. We show the numerical efficiency of the method by comparing it with the existing methods.

Keywords

• Non-linear equations
• monotone equations
• spectral gradient method
• projection method