On Numerical Solution of the Maximum Volume Ellipsoid Problem

In this paper we study practical solution methods for nding the maximum-volume ellipsoid inscribing a given full-dimensional polytope in < n deened by a nite set of linear inequalities. Our goal is to design a general-purpose algorithmic framework that is reliable and eecient in practice. To evaluate the merit of a practical algorithm, we consider two key factors: the computational cost per iteration and the typical number of iterations required for convergence. In addition, numerical stability is also an important factor. We investigate some new formulations upon which we build primal-dual type, interior-point algorithms, and we provide theoretical justiications for the proposed formulations and algorithmic framework. Extensive numerical experiments have shown that one of the new algorithms should be the method of choice among the tested algorithms.