Maximizing the ratio of two convex functions over a convex set

Naval Research Logistics

Volumn 53, Issue 4, 2006, Pages 309-317

  Benson, Harold P ^a  

^a UNIVERSITY OF FLORIDA   (United States)

Author keywords

Branch and bound; Fractional programming; Global optimization; Ratio of convex functions

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; LINEAR PROGRAMMING; PROBLEM SOLVING;

BRANCH AND BOUND; FRACTIONAL PROGRAMMING; RATIO OF CONVEX FUNCTIONS;

SET THEORY;

EID: 33646230555     PISSN: 0894069X     EISSN: 15206750     Source Type: Journal    
DOI: 10.1002/nav.20143     Document Type: Article

References (21)

1. M. Avriel, W.E. Diewert, S. Schaible, and I. Zang, Generalized concavity, Plenum, New York, 1988.
2. H.P. Benson, An outcome space branch and bound-outer approximation algorithm for convex multiplicative programming, J Global Optim 15 (1999), 315-342.
3. H.P. Benson and R. Horst, A branch and bound-outer approximation algorithm for concave minimization over a convex set, Comput Math Appl 21 (1991), 67-76.
4. B.D. Craven, Fractional programming, Heldermann, Berlin, 1988.
5. W. Dinkelbach, On nonlinear fractional programming, Manage Sci 13 (1967), 492-498.
6. J.E. Falk and K.R. Hoffman, A successive underestimation method for concave minimization problems, Math Oper Res 1 (1976), 251-259.
7. J.B.G. Frenk and S. Schaible, "Fractional programming," Encyclopedia of optimization, volume II, C.A. Floudas and P.M. Pardalos (Editors), Kluwer, Dordrecht, 2001, pp. 162-172.
8. J.-Y. Gotoh and H. Konno, Maximization of the ratio of two convex quadratic functions over a polytope, Comp Optim Appl 20 (2001), 43-60.
9. R. Horst, An algorithm for nonconvex programming problems, Math Program 10 (1976), 312-321.
10. R. Horst and H. Tuy, Global optimization: Deterministic approaches, Springer, Berlin, 1990.
11. C. Lemarechal, "Nondifferentiable optimization," Optimization, G.L. Nemhauser, A.H.G. Rinnooy Kan, and M.J. Todd (Editors), North-Holland, Amsterdam, 1989, pp. 529-572.
12. A.W. Lo and A.C. MacKinlay, Maximizing predictability in the stock and bond markets, Macroecon Dynam 1 (1997), 102-134.
13. B. Martos, Nonlinear programming: Theory and methods, North-Holland, Amsterdam, 1975.
14. J.A. Ohlson and W.T. Ziemba, Optimal portfolio policies for an investor with a power utility function facing a log normal securities market, J Fin Quant Anal 11 (1976), 57-71.
15. R.T. Rockafellar, Convex analysis, Princeton University Press, Princeton, NJ, 1970.
16. S. Schaible, "Fractional programming," Handbook of global optimization, R. Horst and P.M. Pardalos (Editors), Kluwer, Dordrecht, 1995, pp. 495-608.
17. S. Schaible, Fractional programming: Applications and algorithms, Eur J Oper Res 7 (1981), 111-120.
18. S. Schaible, Fractional programming - Some recent developments, J Info Optim Sci 10 (1989), 1-14.
19. S. Schaible, Parameter-free convex equivalent and dual programs of fractional programs, Zeits Oper Res 18 (1974), 187-196.
20. N.Z. Shor, Minimization methods for nondifferentiable functions, Springer, Berlin, 1985.
21. I.M. Stancu-Minasian, Fractional programming: Theory, methods and applications, Kluwer, Dordrecht, 1997.