A Primal-Dual Interior-Point Algorithm for Nonlinear Least Squares Constrained Problems

• Autores: M. Fernanda P. Costa, Edite M. G. P. Fernandes
• Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 13, Nº. 1, 2005, págs. 145-166
• Idioma: inglés
• DOI: 10.1007/bf02578992
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• Resumen

  • This paper extends prior work by the authors on solving nonlinear least squares unconstrained problems using a factorized quasi-Newton technique. With this aim we use a primal-dual interior-point algorithm for nonconvex nonlinear program- ming. The factorized quasi-Newton technique is now applied to the Hessian of the Lagrangian function for the transformed problem which is based on a logarithmic barrier formulation. We emphasize the importance of establishing and maintaining symmetric quasi-definiteness of the reduced KKT system. The algorithm then tries to choose a step size that reduces a merit function, and to select a penalty parameter that ensures descent directions along the iterative process. Computa- tional results are included for a variety of least squares constrained problems and preliminary numerical testing indicates that the algorithm is robust and efficient in practice.