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Maximization of the Ratio of Two Convex Quadratic Functions over a Polytope

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Abstract

In this paper, we will develop an algorithm for solving a quadratic fractional programming problem which was recently introduced by Lo and MacKinlay to construct a maximal predictability portfolio, a new approach in portfolio analysis. The objective function of this problem is defined by the ratio of two convex quadratic functions, which is a typical global optimization problem with multiple local optima. We will show that a well-designed branch-and-bound algorithm using (i) Dinkelbach's parametric strategy, (ii) linear overestimating function and (iii) ω-subdivision strategy can solve problems of practical size in an efficient way. This algorithm is particularly efficient for Lo-MacKinlay's problem where the associated nonconvex quadratic programming problem has low rank nonconcave property.

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Authors and Affiliations

  1. Institute of Policy and Planning Sciences, University of Tsukuba, Ibaraki, Japan

    Jun-Ya Gotoh

  2. Department of Industrial and Systems Engineering, Chuo University, Tokyo, Japan

    Hiroshi Konno

Authors
  1. Jun-Ya Gotoh
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  2. Hiroshi Konno
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Gotoh, JY., Konno, H. Maximization of the Ratio of Two Convex Quadratic Functions over a Polytope. Computational Optimization and Applications 20, 43–60 (2001). https://doi.org/10.1023/A:1011219422283

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