最大体積楕円体の中心を用いる確率的切除平面法

概要

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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.
公益社団法人計測自動制御学会の論文