- Improved complexity for maximum volume inscribed ellipsoids K.M. Anstreicher (kurt-anstreicheruiowa.edu) Abstract: Let $\Pcal=\{x | Ax\le b\}$, where $A$ is an $m\times n$ matrix. We assume that $\Pcal$ contains a ball of radius one centered at the origin, and is contained in a ball of radius $R$ centered at the origin. We consider the problem of approximating the maximum volume ellipsoid inscribed in $\Pcal$. Such ellipsoids have a number of interesting applications, including the inscribed ellipsoid method for convex optimization. We reduce the complexity of finding an ellipsoid whose volume is at least a factor $e^{-\epsilon}$ of the maximum possible to $O(m^{3.5}\ln(mR/\epsilon))$ operations, improving on previous results of Nesterov and Nemirovskii, and Khachiyan and Todd. A further reduction in complexity is obtained by first computing an approximation of the analytic center of $\Pcal$. Keywords: Maximum volume inscribed ellipsoid, inscribed ellipsoid method Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming ) Category 2: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: Working paper, Dept. of Management Sciences, University of Iowa, June 2001 Download: [Postscript]Entry Submitted: 06/14/2001Entry Accepted: 06/14/2001Entry Last Modified: 06/14/2001Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.