An efficient algorithm for solving convex-convex quadratic fractional programs

Journal of Optimization Theory and Applications

Volumn 133, Issue 2, 2007, Pages 241-255

  Yamamoto, R ^a,b   Konno, H ^a  

^a CHUO UNIVERSITY   (Japan)

^b MTB Investment Technology Institute Co Ltd   (Japan)

Author keywords

Dinkelbach method; Global optimization; Integer programming; Local search algorithms; Nonconvex quadratic programming problems; Nonlinear fractional programs; Portfolio analysis

Indexed keywords

BRANCH AND BOUND METHOD; INTEGER PROGRAMMING; LOCAL SEARCH (OPTIMIZATION); PROBLEM SOLVING; QUADRATIC PROGRAMMING;

ALGORITHM FOR SOLVING; DINKELBACH'S METHODS; GLOBAL OPTIMISATION; INTEGER PROGRAM- MING; LOCAL SEARCH ALGORITHM; NONCONVEX QUADRATIC PROGRAMMING PROBLEM; NONLINEAR FRACTIONAL PROGRAM; OBJECTIVE FUNCTIONS; PORTFOLIO ANALYSIS; QUADRATIC FUNCTION;

GLOBAL OPTIMIZATION;

EID: 34547240222     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-007-9188-y     Document Type: Article

References (18)

1. Charnes, A., Cooper, W.W.: Programming with linear fractional functions. Nav. Res. Logist. Q. 9, 181-186 (1962)
2. Schaible, S.: Fractional programming II, on Dinkelbach's algorithm. Manag. Sci. 22, 868-873 (1976)
3. Dinkelbach, W.: On nonlinear fractional programming. Manag. Sci. 13, 492-498 (1967)
4. Pardalos, P.M., Phillips, A.T.: Global optimization of fractional programs. J. Glob. Optim. 1, 173-182 (1991)
5. Schaible, S.: Fractional programming. In: Horst, R., Pardalos, P. (eds.) Handbook of Global Optimization. Kluwer Academic, Dordrecht (1995)
6. Lo, A., Mackinlay, C.: Maximizing predictability in the stock and bond markets. Macroecon. Dyn. 1, 102-134 (1997)
7. Gotoh, J., Konno, H.: Maximization of the ratio of two convex quadratic functions over a polytope. Comput. Optim. Appl. 20, 43-60 (2001)
8. Konno, H., Thach, P.T., Tuy, H.: Optimization on Low Rank Nonconvex Structures. Kluwer Academic, Dordrecht (1997)
9. Phong, T.Q., An, L.T.H., Tao, P.D.: Decomposition branch and bound method for globally solving linearly constrained indefinite quadratic minimization problems. Oper. Res. Lett. 17, 215-220 (1995)
10. Konno, H., Yamamoto, R.: Global optimization vs integer programming in portfolio optimization under nonconvex transaction cost. Report ISE03-07, Department of Industrial and System Engineering, Chuo University, Tokyo, Japan (2003)
11. Konno, H., Yamamoto, R.: Integer programming approaches in mean-risk model. Report ISE03-08, Department of Industrial and System Engineering, Chuo University, Tokyo, Japan (2003)
12. Wolsey, L.A.: Integer Programming. Wiley, New York (1998)
13. Bertsekas, D.: Nonlinear Programming, 2nd edn. Athena Scientific, Belmont (1995)
14. Luenberger, D.G.: Nonlinear Programming, 2nd edn. Kluwer Academic, Dordrecht (2003)
15. Dantzig, G.B.: Linear Programming and Extensions. Princeton University Press, Princeton (1963)
16. Ibaraki, T.: Parametric approaches to fractional programs. Math. Program. 26, 345-362 (1983)
17. Sekitani, K., Shi, J.M., Yamamoto, Y.: General fractional programming: minmax convex-convex quadratic case. In: Proceedings of APORS'94, pp. 505-514. World Scientific, Singapore (1995)
18. Gantmacher, F.R.: The Theory of Matrices. Chelsea, New York (1959)