Abstract
This paper considers a problem of nonlinear programming in which the objective function is the ratio of two linear functions and the constraints define a bounded and connected feasible region. Using a coordinate transformation, this problem is transformed into a simpler one, whose geometric interpretation is of particular significance. The transformation leads to a characterization of some special vertices of the feasible region from both the theoretical and operational points of view.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Schaible, S.,Fractional Programing: Applications and Algorithms, European Journal of Operational Research, Vol. 7, pp. 111–120, 1981.
Schaible, S., andIbaraki, T.,Fractional Programming, European Journal of Operational Research, Vol. 12, pp. 325–338, 1983.
Martos, B.,Nonlinear Programming Theory and Methods, North-Holland, Amsterdam, Holland, 1975.
Martos, B.,Hyperbolic Programming, Naval Research Logistics Quarterly, Vol. 11, pp. 135–155, 1964.
Cambini, A., andMartein, L.,A Modified Version of Martos Algorithm for the Linear Fractional Problem, International Workshop on Generalized Concavity, Fractional Programming, and Economic Applications, Pisa, Italy, 1988.
Author information
Authors and Affiliations
Additional information
Communicated by F. Zirilli
Rights and permissions
About this article
Cite this article
Ottaviani, M., Pacelli, G. Fractional programming and characterization of some vertices of the feasible region. J Optim Theory Appl 79, 333–344 (1993). https://doi.org/10.1007/BF00940584
Issue Date:
DOI: https://doi.org/10.1007/BF00940584