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On the choice of parameters for power-series interior point algorithms in linear programming

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Abstract

In this paper we study higher-order interior point algorithms, especially power-series algorithms, for solving linear programming problems. Since higher-order differentials are not parameter-invariant, it is important to choose a suitable parameter for a power-series algorithm. We propose a parameter transformation to obtain a good choice of parameter, called ak-parameter, for general truncated powerseries approximations. We give a method to find ak-parameter. This method is applied to two powerseries interior point algorithms, which are built on a primal—dual algorithm and a dual algorithm, respectively. Computational results indicate that these higher-order power-series algorithms accelerate convergence compared to first-order algorithms by reducing the number of iterations. Also they demonstrate the efficiency of thek-parameter transformation to amend an unsuitable parameter in power-series algorithms.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, 0511, Singapore

    Gongyun Zhao

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  1. Gongyun Zhao
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Work supported in part by the DFG Schwerpunktprogramm “Anwendungsbezogene Optimierung und Steuerung”.

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Zhao, G. On the choice of parameters for power-series interior point algorithms in linear programming. Mathematical Programming 68, 49–71 (1995). https://doi.org/10.1007/BF01585757

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  • DOI: https://doi.org/10.1007/BF01585757

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