A New Hybrid Approach for Solving Large-scale Monotone Nonlinear Equations

Abstract

In this paper, a new hybrid conjugate gradient method for solving monotone nonlinear equations is introduced. The scheme is a combination of the Fletcher-Reeves (FR) and Polak-Ribiére-Polyak (PRP) conjugate gradient methods with the Solodov and Svaiter projection strategy. Using suitable assumptions, the global convergence of the scheme with monotone line search is provided. Lastly, a numerical experiment was used to enumerate the suitability of the proposed scheme for large-scale problems.

Keywords

• global convergence
• line search
• monotone equations
• projection strategy