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

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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.

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Authors and Affiliations

  1. Research Fellow, Department of Decision Sciences and Singapore-MIT Alliance, Associate Professor, Department of Applied Mathematics, National University of Singapore, Hebei University of Technology, Kent Ridge, Tianjin, Singapore, PRC.

    X. W. Liu

  2. Professor, Department of Decision Sciences and Singapore-MIT Alliance, National University of Singapore, Kent Ridge, Singapore

    J. Sun

Authors
  1. X. W. Liu
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  2. J. Sun
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Additional information

Communicated by Z. Q. Luo

This research was partially supported by Grant R-314-000-026/042/057-112 of National University of Singapore and Singapore-MIT Alliance. We thank Professor Khoo Boo Cheong, Cochair of the High Performance Computation Program of Singapore-MIT Alliance, for his support

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Liu, X.W., Sun, J. Global Convergence Analysis of Line Search Interior-Point Methods for Nonlinear Programming without Regularity Assumptions. J Optim Theory Appl 125, 609–628 (2005). https://doi.org/10.1007/s10957-005-2092-4

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