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Global Convergence Analysis of Line Search Interior-Point Methods for Nonlinear Programming without Regularity Assumptions

Author

Listed:
  • X. W. Liu

    (National University of Singapore, Hebei University of Technology)

  • J. Sun

    (National University of Singapore)

Abstract

As noted by Wächter and Biegler (Ref. 1), a number of interior-point methods for nonlinear programming based on line-search strategy may generate a sequence converging to an infeasible point. We show that, by adopting a suitable merit function, a modified primal-dual equation, and a proper line-search procedure, a class of interior-point methods of line-search type will generate a sequence such that either all the limit points of the sequence are KKT points, or one of the limit points is a Fritz John point, or one of the limit points is an infeasible point that is a stationary point minimizing a function measuring the extent of violation to the constraint system. The analysis does not depend on the regularity assumptions on the problem. Instead, it uses a set of satisfiable conditions on the algorithm implementation to derive the desired convergence property.

Suggested Citation

  • X. W. Liu & J. Sun, 2005. "Global Convergence Analysis of Line Search Interior-Point Methods for Nonlinear Programming without Regularity Assumptions," Journal of Optimization Theory and Applications, Springer, vol. 125(3), pages 609-628, June.
    • Handle: RePEc:spr:joptap:v:125:y:2005:i:3:d:10.1007_s10957-005-2092-4
    DOI: 10.1007/s10957-005-2092-4
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