Probabilistic cutting plane technique based on maximum volume ellipsoid center

This paper presents a probabilistic cutting plane technique for solving a robust feasibility problem which is to find a solution satisfying a parameter-dependent convex constraint for all possible parameter values. The proposed algorithm employs random samples of the parameter and maximum volume ellipsoid centers of candidates of the solution set. It is shown that the numbers of updates and random samples are polynomials of the problem size. The algorithm is also extended for solving a robust optimization problem.