Minimal Ellipsoid Circumscribing a Polytope Defined by a System of Linear Inequalities
Journal of Global Optimization
Efficient algorithm for approximating maximum inscribed sphere in high dimensional polytope
Proceedings of the twenty-second annual symposium on Computational geometry
Computation of Minimum-Volume Covering Ellipsoids
Operations Research
Clustering via minimum volume ellipsoids
Computational Optimization and Applications
On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids
Discrete Applied Mathematics
Conditional minimum volume ellipsoid with application to multiclass discrimination
Computational Optimization and Applications
PSwarm: a hybrid solver for linearly constrained global derivative-free optimization
Optimization Methods & Software - GLOBAL OPTIMIZATION
Duality of Ellipsoidal Approximations via Semi-Infinite Programming
SIAM Journal on Optimization
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In this paper we study practical solution methods for finding the maximum volume ellipsoid inscribing a given full-dimensional polytope in $\Re^n$ defined by a finite set of linear inequalities. Our goal is to design a general-purpose algorithmic framework that is reliable and efficient 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 an important factor. We investigate some new formulations upon which we build primal-dual type interior-point algorithms, and we provide theoretical justifications for the proposed formulations and algorithmic framework. Extensive numerical experiments have shown that one of the new algorithms is the method of choice among those tested.