  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) 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.
