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The long-step method of analytic centers for fractional problems

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Abstract

We develop a long-step surface-following version of the method of analytic centers for the fractional-linear problem min{t 0 |t 0 B(x) −A(x) εH, B(x) εK, x εG}, whereH is a closed convex domain,K is a convex cone contained in the recessive cone ofH, G is a convex domain andB(·),A(·) are affine mappings. Tracing a two-dimensional surface of analytic centers rather than the usual path of centers allows to skip the initial “centering” phase of the path-following scheme. The proposed long-step policy of tracing the surface fits the best known overall polynomial-time complexity bounds for the method and, at the same time, seems to be more attractive computationally than the short-step policy, which was previously the only one giving good complexity bounds.

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Authors and Affiliations

  1. Faculty of Industrial Engineering and Management, Technion — The Israel Institute of Technology, 3200, Technion City, Haifa, Israel

    A. Nemirovski

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  1. A. Nemirovski
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The research was partly supported by the Israeli-American Binational Science Foundation (BSF).

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Nemirovski, A. The long-step method of analytic centers for fractional problems. Mathematical Programming 77, 191–224 (1997). https://doi.org/10.1007/BF02614435

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  • DOI: https://doi.org/10.1007/BF02614435

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