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There are special cases of convex problems that can be solved in polynomial time, e.g. a convex QP defined over a simplex. In general, however, convex programming is NP-hard. However, NP-hard by no means means unsolvable. Although theorists would probably cringe at the term, there are NP-hard and what I coin as "NP-harder" problems. What I call an NP-harder ...

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