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

X. W. Liu and J. Sun
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X. W. Liu: National University of Singapore, Hebei University of Technology
J. Sun: National University of Singapore

Journal of Optimization Theory and Applications, 2005, vol. 125, issue 3, No 7, 609-628

Abstract: 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.

Keywords: Nonlinear programming; interior-point methods; convergence (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10957-005-2092-4

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