Hostname: page-component-89b8bd64d-ktprf Total loading time: 0 Render date: 2026-05-06T10:07:29.074Z Has data issue: false hasContentIssue false
  • English
  • Français

Fractional programming duality via geometric programming duality

Published online by Cambridge University Press:  17 February 2009

C. H. Scott  and
T. R. Jefferson
C. H. Scott
Affiliation:
School of Mechanical and Industrial Engineering, University of N.S.W. Kensington, N.S.W. 2033, Australia
T. R. Jefferson
Affiliation:
School of Mechanical and Industrial Engineering, University of N.S.W. Kensington, N.S.W. 2033, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

A duality theory for a class of fractional programs is developed. A fractionalprogram which is non-convex is convexified using a one-to-one transformation. The resulting convex equivalent is then dualized with generalized geometric programming duality.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 21 , Issue 4 , April 1980 , pp. 398 - 401
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Bector, C. R., “Duality in nonlinear fractional programming”, Zeitschrift für Operations Research 17 (1973), 183–193.Google Scholar
[2]Chames, A. and Cooper, W. W., “Programming with linear fractional functionals”,Nav. Res. Log. Quart. 9 (1962), 181–186.Google Scholar
[3]Craven, B. D. and Mond, B., “The dual of a fractional linear program”, J. Math. Anal. Appl. 42 (1973), 507–512.CrossRefGoogle Scholar
[4]Craven, B. D., Mathematical programming and control theory (Chapman and Hall, 1978).CrossRefGoogle Scholar
[5]Jagannathan, R., “Duality for nonlinear fractional programs”, Zeitschrift für Operations Research 17 (1973), 1–3.Google Scholar
[6]Manas, M., “On transformation of quasi-convex programming problems”, Ekonomicko Matematicky Obzor 4 (1968), 93–99.Google Scholar
[7]Mond, B. and Craven, B. D., “A note on mathematical programming with fractional objective functions”, Nav. Res. Log. Quart. 20 (1973), 577–581.CrossRefGoogle Scholar
[8]Peterson, E. L., “Geometric programming”, SIAM Review 18 (1976), 1–52.CrossRefGoogle Scholar
[9]Rani, O. and Kaul, R. N., “Duality theorems for a class of non-convex programming problems”, J. Optim. Theory Applic. 11 (1973), 305–308.CrossRefGoogle Scholar
[10]Rockafellar, T. R., Convex analysis (Princeton: Princeton University Press, 1970).CrossRefGoogle Scholar
[11]Schaible, S., “Parameter free convex equivalent and dual programs of fractional programming problems”, Zeitschrift für Operations Research 18 (1974), 187–196.Google Scholar
[12]Schaible, S., “Fractional programming. I. Duality”, Management Science 22 (1976), 858–862.CrossRefGoogle Scholar
[13]Schaible, S., “Duality in fractional programming: a unified approach”, Operations Research 24 (1976), 452–561.CrossRefGoogle Scholar