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A class of polynomial variable metric algorithms for linear optimization

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Abstract

In the paper, the behaviour of interior point algorithms is analyzed by using a variable metric method approach. A class of polynomial variable metric algorithms is given achieving O ((n/β)L) iterations for solving a canonical form linear optimization problem with respect to a wide class of Riemannian metrics, wheren is the number of dimensions and β a fixed value. It is shown that the vector fields of several interior point algorithms for linear optimization is the negative Riemannian gradient vector field of a linear a potential or a logarithmic barrier function for suitable Riemannian metrics.

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Authors and Affiliations

  1. Laboratory of Operations Research and Decision Systems, Computer and Automation Institute, Hungarian Academy of Sciences, P.O. Box 63, H-1518, Budapest, Hungary

    T. Rapcsák & T. T. Thang

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  1. T. Rapcsák
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  2. T. T. Thang
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Additional information

Research Partially supported by the Hungarian National Research Foundation, Grant Nos. OTKA-T016413 and OTKA-2116.

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Rapcsák, T., Thang, T.T. A class of polynomial variable metric algorithms for linear optimization. Mathematical Programming 74, 319–331 (1996). https://doi.org/10.1007/BF02592202

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  • DOI: https://doi.org/10.1007/BF02592202

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