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A unified approach to the implementation of several restart fixed point algorithms and a new variable dimension algorithm

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Abstract

We present a unified description of a class of restart fixed point algorithms including Merrill's method and several variable dimension algorithms for their implementation on computers. Based on this description we show that some pivot-saving techniques originally developed for the homotopy methods can be applied to the class. We also propose a new variable dimension algorithm having 3n-1 rays along which we can move toward a solution. Some numerical comparisons of the simplicial restart algorithms, Merrill's method, the 2n-method, the octahedral method and the new one, support that the latter two methods are more efficient than the others.

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Authors and Affiliations

  1. Department of Information Sciences, Tokyo Institute of Technology, Oh-okayama, Meguro, 152, Tokyo, Japan

    Masakazu Kojima

  2. Institute of Socio-Economic Planning, University of Tsukuba, Sakura, 305, Ibaraki, Japan

    Yoshitsugu Yamamoto

Authors
  1. Masakazu Kojima
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  2. Yoshitsugu Yamamoto
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Kojima, M., Yamamoto, Y. A unified approach to the implementation of several restart fixed point algorithms and a new variable dimension algorithm. Mathematical Programming 28, 288–328 (1984). https://doi.org/10.1007/BF02612336

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  • DOI: https://doi.org/10.1007/BF02612336

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