-

 

 

 




Optimization Online





 

Improved complexity for maximum volume inscribed ellipsoids

K.M. Anstreicher (kurt-anstreicher***at***uiowa.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: 06/14/2001
Entry Accepted: 06/14/2001
Entry Last Modified: 06/14/2001

Modify/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
Mathematical Programming Society