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Sufficient optimality criterion for linearly constrained, separable concave minimization problems

Illes, T. and Nagy, Á.B. (2005) Sufficient optimality criterion for linearly constrained, separable concave minimization problems. Journal of Optimization Theory and Applications, 125 (3). pp. 559-575. ISSN 0022-3239

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A sufficient optimality criterion for linearly-constrained concave minimization problems is given in this paper. Our optimality criterion is based on the sensitivity analysis of the relaxed linear programming problem. The main result is similar to that of Phillips and Rosen (Ref. 1); however, our proofs are simpler and constructive. In the Phillips and Rosen paper (Ref. 1), they derived a sufficient optimality criterion for a slightly different linearly-constrained concave minimization problem using exponentially many linear programming problems. We introduce special test points and, using these for several cases, we are able to show optimality of the current basic solution. The sufficient optimality criterion described in this paper can be used as a stopping criterion for branch-and-bound algorithms developed for linearly-constrained concave minimization problems.