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Convergence behavior of interior-point algorithms

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Abstract

We show that most interior-point algorithms for linear programming generate a solution sequence in which every limit point satisfies the strict complementarity condition. These algorithms include all path-following algorithms and some potential reduction algorithms. The result also holds for the monotone complementarity problem if a strict complementarity solution exists. In general, the limit point is a solution that maximizes the number of its nonzero components among all solutions.

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Authors and Affiliations

  1. Department of Management Sciences, The University of Iowa, Iowa City, IA, USA

    Osman Güler & Yinyu Ye

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  1. Osman Güler
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  2. Yinyu Ye
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Research supported in part by NSF Grant DDM-8922636, the Iowa Business School Summer Grant, and the Interdisciplinary Research Grant of the University of Iowa Center for Advanced Studies.

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Güler, O., Ye, Y. Convergence behavior of interior-point algorithms. Mathematical Programming 60, 215–228 (1993). https://doi.org/10.1007/BF01580610

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  • DOI: https://doi.org/10.1007/BF01580610

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