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Solving systems of nonlinear equations and inequalities is ofcritical importance in many engineering problems. In general, theexistence of inequalities in the problem adds to its difficulty.We propose a new projected Hessian Gauss-Newton algorithm forsolving general nonlinear systems of equalities and inequalities.The algorithm uses the projected Gauss-Newton Hessian inconjunction with an active set strategy that identifies activeinequalities and a trust-region globalization strategy thatensures convergence from any starting point. We also present aglobal convergence theory for the proposed algorithm

A projected Hessian Gauss-Newton algorithm for solving systems of nonlinear equations and inequalities