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On the continuity of the maximum in parametric linear programming

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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.

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References

  1. 1.

    Dinkelbach, W.,Sensitivitätsanalysen und Parametrische Programmierung, Springer-Verlag, Berlin, Germany, 1969.

  2. 2.

    Bereanu, B.,On Stochastic Linear Programming, IV, Proceedings of the Fourth Conference on Probability Theory, Brasov, Romania, 1973.

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Additional information

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.

Communicated by G. L. Nemhauser

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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

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Key Words

  • Linear programming
  • parametric linear programming
  • semicontinuity
  • operations research
  • inequality theory