On the existence of optimal solutions to integer and mixed-integer programming problems

Abstract

The purpose of this paper is to present sufficient conditions for the existence of optimal solutions to integer and mixed-integer programming problems in the absence of upper bounds on the integer variables. It is shown that (in addition to feasibility and boundedness of the objective function) (1) in the pure integer case a sufficient condition is that all of the constraints (other than non-negativity and integrality of the variables) beequalities, and (2) that in the mixed-integer caserationality of the constraint coefficients is sufficient. Some computational implications of these results are also given.

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Sponsored by the United States Army under Contract No. DA-31-124-ARO-D-462.

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Meyer, R.R. On the existence of optimal solutions to integer and mixed-integer programming problems. Mathematical Programming 7, 223–235 (1974). https://doi.org/10.1007/BF01585518

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Keywords

  • Objective Function
  • Mathematical Method
  • Programming Problem
  • Integer Variable
  • Integer Case