© Hindawi Publishing Corp. A PROJECTED HESSIAN GAUSS-NEWTON ALGORITHM FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS AND INEQUALITIES

Abstract. Solving systems of nonlinear equations and inequalities is of critical impor-tance in many engineering problems. In general, the existence of inequalities in the prob-lem adds to its difficulty. We propose a new projected Hessian Gauss-Newton algorithm for solving general nonlinear systems of equalities and inequalities. The algorithm uses the projected Gauss-Newton Hessian in conjunction with an active set strategy that identi-fies active inequalities and a trust-region globalization strategy that ensures convergence from any starting point. We also present a global convergence theory for the proposed algorithm. 2000 Mathematics Subject Classification. Primary 65F15, 65G50. 1. Introduction. Th