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Maximization of the ratio of two convex quadratic functions over a polytope. (English) Zbl 0984.90046

Summary: We develop an algorithm for solving a quadratic fractional programming problem 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 show that a well-designed branch-and-bound algorithm using (i) Dinkelbach’s parametric strategy, (ii) linear overestimating function and (iii) \(\omega\)-subdivision strategy can solve problems of practical size in an efficient way. This algorithm is particularly efficient for Lo-MacKinlay’s problem in which the associated nonconvex quadratic programming problem has low rank nonconcave property.

MSC:

90C32 Fractional programming
52A41 Convex functions and convex programs in convex geometry
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
91B28 Finance etc. (MSC2000)
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