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Probabilistic analytic center cutting plane method with multiple cuts

A probabilistic analytic center cutting plane method with multiple cuts is proposed for a class of robust feasibility problems which is to find a solution satisfying a set of parameter dependent convex constraints for all possible parameter values. In particular, a new update rule is presented for constructing a smaller polytope which contains the intersection among a previous polytope and half spaces determined by given multiple subgradients. This modification could lead to fast convergence of proposed algorithm.