Gotoh, Jun-Ya; Konno, Hiroshi Maximization of the ratio of two convex quadratic functions over a polytope. (English) Zbl 0984.90046 Comput. Optim. Appl. 20, No. 1, 43-60 (2001). 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. Cited in 22 Documents 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) Keywords:fractional programming; Dinkelbach’s approach; branch and bound algorithm; global optimization; maximizing predictability portfolio PDFBibTeX XMLCite \textit{J.-Y. Gotoh} and \textit{H. Konno}, Comput. Optim. Appl. 20, No. 1, 43--60 (2001; Zbl 0984.90046) Full Text: DOI