Abstract
We propose a moment relaxation for two problems, the separation and covering problems with semialgebraic sets generated by a polynomial of degree $d$. We show that (a) the optimal value of the relaxation finitely converges to the optimal value of the original problem, when the moment order $r$ increases, and (b) after performing some small perturbation of the original problem, convergence can be achieved with $r=d$. We further provide a practical iterative algorithm that is computationally tractable for large datasets and present encouraging computational results.
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