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On the Newton Interior-Point Method for Nonlinear Programming Problems

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  • C. Durazzi

    (Università di Padova)

Abstract

Interior-point methods have been developed largely for nonlinear programming problems. In this paper, we generalize the global Newton interior-point method introduced in Ref. 1 and we establish a global convergence theory for it, under the same assumptions as those stated in Ref. 1. The generalized algorithm gives the possibility of choosing different descent directions for a merit function so that difficulties due to small steplength for the perturbed Newton direction can be avoided. The particular choice of the perturbation enables us to interpret the generalized method as an inexact Newton method. Also, we suggest a more general criterion for backtracking, which is useful when the perturbed Newton system is not solved exactly. We include numerical experimentation on discrete optimal control problems.

Suggested Citation

  • C. Durazzi, 2000. "On the Newton Interior-Point Method for Nonlinear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 104(1), pages 73-90, January.
    • Handle: RePEc:spr:joptap:v:104:y:2000:i:1:d:10.1023_a:1004624721836
    DOI: 10.1023/A:1004624721836
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    References listed on IDEAS

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    1. S. Bellavia, 1998. "Inexact Interior-Point Method," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 109-121, January.
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    Cited by:

    1. C. Durazzi & V. Ruggiero & G. Zanghirati, 2001. "Parallel Interior-Point Method for Linear and Quadratic Programs with Special Structure," Journal of Optimization Theory and Applications, Springer, vol. 110(2), pages 289-313, August.

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