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International Journal of Mathematics and Mathematical Sciences
Volume 25, Issue 6, Pages 397-409
http://dx.doi.org/10.1155/S0161171201002290

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

1Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt
2Department of Mathematics and Computer Science, Kuwait University, Kuwait

Received 23 December 1998

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Solving systems of nonlinear equations and inequalities is of critical importance in many engineering problems. In general, the existence of inequalities in the problem 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 identifies 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.