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Optimization problems with algebraic solutions: Quadratic fractional programs and ratio games

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Abstract

A mathematical program with a rational objective function may have irrational algebraic solutions even when the data are integral. We suggest that for such problems the optimal solution will be represented as follows: If λ* denotes the optimal value there will be given an intervalI and a polynomialP(λ) such thatI contains λ* and λ* is the unique root ofP(λ) inI. It is shown that with this representation the solutions to convex quadratic fractional programs and ratio games can be obtained in polynomial time.

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Authors and Affiliations

  1. University of Texas at Dallas, 75080, Richardson, TX, USA

    R. Chandrasekaran

  2. Statistics Department, Tel Aviv University, 69978, Tel Aviv, Israel

    A. Tamir

Authors
  1. R. Chandrasekaran
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  2. A. Tamir
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Chandrasekaran, R., Tamir, A. Optimization problems with algebraic solutions: Quadratic fractional programs and ratio games. Mathematical Programming 30, 326–339 (1984). https://doi.org/10.1007/BF02591937

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  • DOI: https://doi.org/10.1007/BF02591937

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