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4

In the specific problem you ask about (unlike Richard's more general answer), it turns out that you can relax the $=$ constraint into a $\leq$ without changing the optimal value, and that the resulting convex problem can be solved with the CVX software Richard mentioned. Details: Intuitively the relaxation is possible since if the function had arc length ...

2

I think the meat of your question is: Are there numerical packages that can take an integral objective and some arbitrary constraints and give you a solution? The answer is: mostly, no. However, a few packages, such as GPOPS, JuMP, and PyOMO, have facilities for this which sometimes work if your problem is of the right form. For particular classes of ...

1

For general matrices $A$, I believe that the problem is not solvable and have heard people say that it is NP with $N$ equal to the number of positive eigenvalues of $A$. That's because you are trying to find the maximum of a convex function on the unit hypercube, which has $2^N$ corner points. But for your particular case, the problem is easy to solve. ...

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