On the continuity of the maximum in parametric linear programming

  • D. H. Martin


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.

Key Words

Linear programming parametric linear programming semicontinuity operations research inequality theory 


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  1. 1.
    Dinkelbach, W.,Sensitivitätsanalysen und Parametrische Programmierung, Springer-Verlag, Berlin, Germany, 1969.MATHCrossRefGoogle Scholar
  2. 2.
    Bereanu, B.,On Stochastic Linear Programming, IV, Proceedings of the Fourth Conference on Probability Theory, Brasov, Romania, 1973.Google Scholar

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • D. H. Martin
    • 1
  1. 1.Department of Mathematics and Applied MathematicsUniversity of NatalDurbanSouth Africa

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