Global inexact quasi-Newton method for nonlinear system of equations with constraints

摘要

In this paper, we propose a Projected Inexact Quasi-Newton Method (PIQN) to solve nonlinear systems of equations with nonnegative constraints and we develop its respective global convergence theory. Particularly, we show that the method enjoys superlinear convergence rate. In addition, we show the good numerical performance of the method when applied to problems that arise in chemistry, engineering and mathematics. We highlight the efficiency of the method to solve Nonlinear Complementarity Problems (NCP), which appear in many application fields and are recognized as hard problems.