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Given a polytope and an arbitrary subset of its vertices, we show how to construct a differentiable concave function that assumes any arbitrary value within a specified e-tolerance at each vertex of the subset, with each vertex in the subset a strong local constrained minimum. We also show how this construction method can be used to generate test problems for linearly constrained concave minimization algorithms.

Technical Note—Construction of Difficult Linearly Constrained Concave Minimization Problems