A projected Hessian Gauss-Newton algorithm for solving systems of nonlinear equations and inequalities. (8th February 2001)

• Record Type: Journal Article
• Authors: El-Alem, Mahmoud M.; Abdel-Aziz, Mohammedi R.; El-Bakry, Amr S.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 25:Number 6(2001)
• Page Start: 397
• Page End: 409
• Publication Date: 2001-02-08
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171201002290
• Languages: English
• ISSNs: 0161-1712

Abstract

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.