Extending the Applicability of Newton’s Algorithm with Projections for Solving Generalized Equations

Abstract

A new technique is developed to extend the convergence ball of Newton’s algorithm with projections for solving generalized equations with constraints on the multidimensional Euclidean space. This goal is achieved by locating a more precise region than in earlier studies containing the solution on which the Lipschitz constants are smaller than the ones used in previous studies. These advances are obtained without additional conditions. This technique can be used to extend the usage of other iterative algorithms. Numerical experiments are used to demonstrate the superiority of the new results.