We propose a moment relaxation for two problems, the separation and covering problem with semi-algebraic 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) there exist probability measures such that the moment relaxation is equivalent to the original problem with r = d. We further provide a practical iterative algorithm that is computationally tractable for large datasets and present encouraging computational results.
Citation
January 2007