Sufficient optimality criteria for linearly constrained, concave minimization problems is given in this paper. Our optimality criteria is based on the sensitivity analysis of the relaxed linear programming problem. Our main result is similar to that of Phillips and Rosen (1993), however our proofs are simpler and constructive. Phillips and Rosen (1993) in their paper derived sufficient optimality criteria for a slightly different, linearly constrained, concave minimization problem using exponentially many linear programming problems. We introduced special test points and using these, for several cases, we are able to show the optimality of the current basic solution. The sufficient optimality criteria, described in this paper, can be used as a stopping criteria for branch and bound algorithms developed for linearly constrained, concave minimization problems.
Operations Research Reports 2003-02, Department of Operations Research, Eotvos Lorand University of Sciences, H-1117 Budapest, Pazmany Peter setany 1/C, Hungary; December, 2003