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The Complexity of High-Order Interior-Point Methods for Solving Sufficient Complementarity Problems

  • Josef Stoer
  • Martin Wechs
Conference paper

Abstract

Recently the authors of this paper and S. Mizuno described a class of infeasible-interior-point methods for solving linear complementarity problems that are sufficient in the sense of Cottle, Pang and Venkateswaran [1]. It was shown that these methods converge superlinearly with an arbitrarily high order even for degenerate problems or problems without strictly complementary solution. In this paper we report on some recent results on the complexity of these methods. We outline a proof that these methods need at most \(\mathcal{O}\left( {(1 + \kappa )\sqrt {n|\log \varepsilon |} } \right)\) steps to compute an ε-solution, if the problem has strictly interior points. Here, к is the sufficiency parameter of the complementarity problem.

Keywords

Complementarity Problem Linear Complementarity Problem Feasible Point Interior Point Method Interior Point Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Josef Stoer
    • 1
  • Martin Wechs
    • 1
  1. 1.Institut für Angewandte Mathematik und StatistikUniversität WürzburgWürzburgGermany

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