複数の勾配を用いる確率的楕円体法

抄録

A stochastic ellipsoid 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 ellipsoid which contains the intersection of a previous ellipsoid and strips determined by given multiple gradients. A quantitative analysis of the volume of the updated ellipsoid is also provided, which leads to a further modification of the algorithm achieving fast convergence.