On the Existence of Optimal Solutions to Integer and Mixed-Integer Programming Problems.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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The purpose of the 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 in the pure integer case a sufficient condition is that all of the constraints other than non-negativity and integrality of the variables be equalities, and that in the mixed-integer case rationality of the constraint coefficients is sufficient. Some computational implications of these results are also given. Author
- Operations Research