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

Author

Listed:
  • Mahmoud M. El-Alem
  • Mohammedi R. Abdel-Aziz
  • Amr S. El-Bakry

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.

Suggested Citation

  • Mahmoud M. El-Alem & Mohammedi R. Abdel-Aziz & Amr S. El-Bakry, 2001. "A projected Hessian Gauss-Newton algorithm for solving systems of nonlinear equations and inequalities," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 25, pages 1-13, January.
    • Handle: RePEc:hin:jijmms:356386
    DOI: 10.1155/S0161171201002290
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