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Dec 19, 2014 at 3:38 comment added Michael Grant Indeed, I would not tag this as convex-optimization or linear-programming. It is most certainly neither. This is quite a difficult problem and I am unaware of any good heuristics (not that I would know them all!)
Dec 18, 2014 at 16:11 comment added Nathaniel Johnston If you replace the constraint $|x_i| = 1$ with $|x_i| \leq 1$ then it becomes a true convex optimization problem (a semidefinite program, even) and becomes easy to solve. It won't agree with the minimum that you're after in general, but at least will give you a nontrivial lower bound on it.
Dec 18, 2014 at 15:31 answer added Dima Pasechnik timeline score: 2
Dec 18, 2014 at 14:38 history edited Dima Pasechnik CC BY-SA 3.0
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Dec 18, 2014 at 12:53 review First posts
Dec 18, 2014 at 12:57
Dec 18, 2014 at 12:52 history asked Denny CC BY-SA 3.0