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On the Complexity of a Mehrotra-Type Predictor-Corrector Algorithm

  • Ana Paula Teixeira
  • Regina Almeida
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7335)

Abstract

Based on the good computational results of the feasible version of the Mehrotra’s predictor-corrector variant algorithm presented by Bastos and Paixão, in this paper we discuss its complexity. We prove the efficiency of this algorithm by showing its polynomial complexity and, consequently, its Q-linearly convergence.

We start by proving some technical results which are used to discuss the step size estimate of the algorithm.

It is shown that, at each iteration, the step size computed by this Mehrotra’s predictor-corrector variant algorithm is bounded below, for n ≥ 2, by \(\frac{1}{200 n^4};\) consequently proving that the algorithm has O(n 4 |log(ε)|) iteration complexity.

Keywords

Linear Programming predictor-corrector variant interior-point methods Mehrotra-type algorithm polynomial complexity Q-linear convergence 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ana Paula Teixeira
    • 1
    • 2
  • Regina Almeida
    • 1
    • 3
  1. 1.Department of MathematicsUniversity of Trás-os-Montes e Alto DouroVila RealPortugal
  2. 2.CIO. Faculty of SciencesUniversity of LisbonPortugal
  3. 3.CIDMAUniversity of AveiroPortugal

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