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

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 equaliti...

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Bibliographic Details
Published inInternational journal of mathematics and mathematical sciences Vol. 25; no. 6; pp. 397 - 409
Main Authors El-Alem, Mahmoud M, Abdel-Aziz, Mohammedi R, El-Bakry, Amr S
Format Journal Article
LanguageEnglish
Published Hindawi Limited 01.01.2001
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0161-1712
1687-0425
DOI:10.1155/S0161171201002290