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On the existence of duality gaps for mixed integer programming

Only a few theoretical studies of surrogate duality have been carried out since Greenberg and Pierskalla's comprehensive work. Recently, Ram and Karwan examined surrogate duality, and exemplified the existence of surrogate duality gaps for a class of mixed integer programming problems. In this paper, we show that the surrogate duality gaps may exist even for integer programming problems and present necessary sufficient conditions for surrogate (or Langrangion) duality gaps to occur. Then, we extend the results for a class of mixed integer programming problems.