Global optimization algorithm for the nonlinear sum of ratios problem

Journal of Optimization Theory and Applications

Volumn 112, Issue 1, 2002, Pages 1-29

  Benson, H P ^a  

^a UNIVERSITY OF FLORIDA   (United States)

Author keywords

branch and bound algorithms; fractional programming; Global optimization; sum of ratios

Indexed keywords

BRANCH AND BOUND METHOD; CONVEX OPTIMIZATION;

BRANCH AND BOUND SEARCH; BRANCH-AND-BOUND ALGORITHMS; CONVEX PROGRAMMING PROBLEMS; DECISION VARIABLES; FRACTIONAL PROGRAMMING; GLOBAL OPTIMISATION; GLOBAL OPTIMIZATION ALGORITHM; OBJECTIVE FUNCTIONS; SUM OF RATIOS; SUM-OF-RATIOS PROBLEM;

GLOBAL OPTIMIZATION;

EID: 9744254460     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1013072027218     Document Type: Article

References (24)

1. ALMOGY, Y., and LEVIN, O., Parametric Analysis of a Multi-Stage Stochastic Shipping Problem, Proceedings of the 5th IFORS Conference, pp. 359-370, 1964.
2. COLANTONI, C. S., MANES, R. P., and WHINSTON, A., Programming, Profit Rates, and Pricing Decisions, Accounting Review, Vol. 44, pp. 467-481, 1969.
3. KONNO, H., and INORI, M., Bond Portfolio Optimization by Bilinear Fractional Programming, Journal of the Operations Research Society of Japan, Vol. 32, pp. 143-158, 1989.
4. KONNO, H., and WATANABE, H., Bond Portfolio Optimization Problems and Their Application to Index Tracking: A Partial Optimization Approach, Journal of the Operations Research Society of Japan, Vol. 39, pp. 295-306, 1996.
5. SCHAIBLE, S., Fractional Programming, Handbook of Global Optimization, Edited by R. Horst and P. M. Pardalos, Kluwer Academic Publishers, Dordrecht, Holland, 1995.
6. SCHAIBLE, S., Fractional Programming with Sums of Ratios, Working Paper 83, University of Pisa, 1994.
7. SCHAIBLE, S., A Note on the Sum of a Linear and Linear Fractional Function, Naval Research Logistics Quarterly, Vol. 24, pp. 691-693, 1977.
8. CAMBINI, A., MARTEIN, L., and SCHAIBLE, S., On Maximizing a Sum of Ratios, Journal of Information and Optimization Sciences, Vol. 10, pp. 65-79, 1989.
9. KONNO, H., YAJIMA, Y., and MATSUI, T., Parametric Simplex Algorithms for Solving a Special Class of Nonconvex Minimization Problems, Journal of Global Optimization, Vol. 1, pp. 65-81, 1991.
10. FALK, J. E., and PALOCSAY, S. W., Image Space Analysis of Generalized Fractional Programs, Journal of Global Optimization, Vol. 4, pp. 63-88, 1994.
11. KONNO, H., and YAMASHITA, H., Minimizing Sums and Products of Linear Fractional Functions over a Polytope, Naval Research Logistics, Vol. 46, pp. 583-596, 1999.
12. KONNO, H., and FUKAISHI, K., A Branch-and-Bound Algorithm for Solving Low-Rank Linear Multiplicative and Fractional Programming Problems, Journal of Global Optimization, Vol. 18, pp. 283-299, 2000.
13. KUNO, T., A Branch-and-Bound Algorithm for Maximizing the Sum of Several Linear Ratios, Report ISE-TR-00-175, University of Tsukuba, 2000.
14. KONNO, H., and ABE, N., Minimization of the Sum of Three Linear Fractional Functions, Journal of Global Optimization, Vol. 15, pp. 419-432, 1999.
15. KONNO, H., KUNO, T., and YAJIMA, Y., Global Minimization of a Generalized Convex Multiplicative Function, Journal of Global Optimization, Vol. 4, pp. 47-62, 1994.
16. QUESADA, I., and GROSSMANN, I., A Global Optimization Algorithm for Linear Fractional and Bilinear Programs, Journal of Global Optimization, Vol. 6, pp. 39-76, 1995.
17. DUR, M., HORST, R., and THOAI, N. V., Solving Sum-of-Ratios Fractional Programs Using Efficient Points, Optimization (to appear).
18. FREUND, R. W., and JARRE, F., Solving the Sum-of-Ratios Problem by an Interior-Point Method, Journal of Global Optimization, Vol. 19, pp. 83-102, 2001.
19. HORST, R., and TUY, H., Global Optimization: Deterministic Approaches, 2nd Edition, Springer Verlag, Berlin, Germany, 1993.
20. DANTZIG, G. B., FOLKMAN, J., and SHAPIRO, N., On the Continuity of the Minimum Set of a Continuous Function, Journal of Mathematical Analysis and Applications, Vol. 17, pp. 519-548, 1967.
21. BAZARAA, M. S., SHERALI, H. D., and SHETTY, C. M., Nonlinear Programming: Theory and Algorithms, John Wiley and Sons, New York, NY, 1993.
22. BENSON, H. P., An Outcome Space Branch-and-Bound Outer-Approximation Algorithm for Convex Multiplicative Programming, Journal of Global Optimization, Vol. 15, pp. 315-342, 1999.
23. BENSON, H. P., Concave Minimization: Theory, Applications, and Algorithms, Handbook of Global Optimization, Edited by R. Horst and P. M. Pardalos, Kluwer Academic Publishers, Dordrecht, Holland, 1995.
24. BENSON, H. P., Deterministic Algorithms for Constrained Concave Minimization: A Unified Critical Survey, Naval Research Logistics, Vol. 43, pp. 765-795, 1996.