Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
Stochastic Ellipsoid Methods with Multiple Cuts
Takayuki WADAYasumasa FUJISAKI
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2008 Volume 21 Issue 5 Pages 145-150

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Abstract

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.

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