International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 6, Pages 397-409
doi: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 Mahmoud M. El-Alem et al. 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.