For one, the KKT conditions still apply. But in general even simple problems can be tough. For instance, maximizing a p-norm over a fairly nice type of convex polytope ("parallelotope") is NP hard -- see Bodlaender et al, "Computational Complexity of Norm Maximization." The general wisdom is: minimizing convex functions is easy; maximizing convex functions (equivalently, minimizing concave functions) is hard, though there are obviously exceptions.
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For one, the KKT conditions still apply. But in general even simple problems can be tough. For instance, maximizing a p-norm over a fairly nice type of convex polytope ("parallelotope") is NP hard -- see Bodlaender et al, "Computational Complexity of Norm Maximization." |
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