Abstract
For the widest class of parametric linear programs with continuous dependence of coefficients on parameters, the following theorem is proven: for any parameter vectort 0 in the domain of definition of the maximum, if the set of optimal solutions is bounded, then the maximum is upper semicontinuous att 0. If the same proviso is met also in the dual program, then the maximum must be continuous att 0.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Dinkelbach, W.,Sensitivitätsanalysen und Parametrische Programmierung, Springer-Verlag, Berlin, Germany, 1969.
Bereanu, B.,On Stochastic Linear Programming, IV, Proceedings of the Fourth Conference on Probability Theory, Brasov, Romania, 1973.
Author information
Authors and Affiliations
Additional information
Communicated by G. L. Nemhauser
The writer records his appreciation and thanks to Mr. R. A. B. Bond, University of Natal, Durban, South Africa, who stimulated the writer's interest in some of the problems of mathematical programming.
Rights and permissions
About this article
Cite this article
Martin, D.H. On the continuity of the maximum in parametric linear programming. J Optim Theory Appl 17, 205–210 (1975). https://doi.org/10.1007/BF00933875
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00933875