An Evolutionary Approach to Constructing the Minimum Volume Ellipsoid Containing a Set of Points and the Maximum Volume Ellipsoid Embedded in a Set of Points

Abstract

Abstract Given a set of points C = {x 1, x 2, …, xm } ⊆ Rn , what is the minimum volume ellipsoid that encloses it? Equally interestingly, one may ask: What is the maximum volume ellipsoid that can be embedded in the set of points without containing any? These problems have a number of applications beside being interesting in their own right. In this paper we review the important results concerning these and suggest an evolutionary-type approach for their solution. We will also highlight computational results.