New Sufficient Optimality Conditions for Integer Programming and Their Application

Abstract

The purpose of this report is to present a new class of sufficient optimality conditions for pure and mixed integer programming problems. Some of the sets of sufficient conditions presented can be thought of a generalizations of optimality conditions based on primal-dual complementarity in linear programming, and these sufficient conditions are particularly useful for the construction of difficult integer programming problems with known optimal solutions. These problems may then be used to test and/or "benchmark" integer programming codes.