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Nonlinear objectives, nonlinear constraints, non-convex objective, non-convex feasible region.

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How to solve such an optimization problem

I would try geometric programming. https://web.stanford.edu/~boyd/papers/pdf/gp_tutorial.pdf Maximize $$\sum_{S \subset \{1,2,..., N\},\\ |S| = K} \prod_{i<j,\\ i,j \in S} (x_j - x_i)^2.$$ such that $ …
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