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

Authors:
Jun-Ya Gotoh;Hiroshi Konno
Affiliations:
Institute of Policy and Planning Sciences, University of Tsukuba, Ibaraki, Japan;Department of Industrial and Systems Engineering, Chuo University, Tokyo, Japan
Venue:
Computational Optimization and Applications
Year:
2001

Citing 1
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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.