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Positivity

, Volume 6, Issue 3, pp 261–274 | Cite as

Subdifferentiability and the Duality Gap

  • N. E. Gretsky
  • J. M. Ostroy
  • W. R. Zame
Article

Abstract

We point out a connection between sensitivity analysis and the fundamental theorem of linear programming by characterizing when a linear programming problem has no duality gap. The main result is that the value function is subdifferentiable at the primal constraint if and only if there exists an optimal dual solution and there is no duality gap. To illustrate the subtlety of the condition, we extend Kretschmer's gap example to construct (as the value function of a linear programming problem) a convex function which is subdifferentiable at a point but is not continuous there. We also apply the theorem to the continuum version of the assignment model.

duality gap value function subdifferentiability assignment model 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • N. E. Gretsky
    • 1
  • J. M. Ostroy
    • 2
  • W. R. Zame
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaRiversideU.S.A.
  2. 2.Department of EconomicsUniversity of CaliforniaLos AngelesU.S.A.

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