Abstract
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. It is shown that the numbers of updates and random samples are polynomials of the problem size, where the numbers are much smaller than those of the other randomized algorithms, especially the probabilistic cutting plane method based on analytic center. This feature of the algorithm is illustrated through a numerical example.
