A double-projection-based algorithm for large-scale nonlinear systems of monotone equations

Abstract

In this paper, we propose a derivative free algorithm for solving large-scale nonlinear systems of monotone equations which combines a new idea of projection methodology with a line search strategy, while an improvement in the projection step is exerted. At each iteration, the algorithm constructs two appropriate hyperplanes which strictly separate the current approximation from the solution set of the problem. Then the new approximation is determined by projecting the current point onto the intersection of two halfspaces that are constructed by these hyperplanes and contain the solution set of the problem. Under some mild conditions, the global convergence of the algorithm is established. Preliminary numerical results indicate that the proposed algorithm is promising.