Published Online: 15 FEB 2011
Copyright © 2010 John Wiley & Sons, Inc. All rights reserved.
Wiley Encyclopedia of Operations Research and Management Science
How to Cite
Takahashi, R. H. C. 2011. Ellipsoidal Algorithms. Wiley Encyclopedia of Operations Research and Management Science. .
- Published Online: 15 FEB 2011
This article reviews the ellipsoidal algorithms (EAs), starting from its working principles, and then presenting the basic EA and some deep cut variations in a constructive manner. The classes of problems for which the EAs are guaranteed to converge to the exact solutions (linear problems, convex problems, and quasi-convex problems) are stated in first place. The general principle of cutting-plane branch-and-cut operation, that is valid for such classes of problems, is presented. The basic EA is stated, as an instance of such principles, and the convergence properties of this version of EA are discussed. The basic EA is then reformulated, with the inclusion of the deep cuts, which accelerate the convergence. Specific forms of deep cuts that can be applied to linear- and convex problems are presented. Some further implementation issues in EAs are briefly discussed, and some references are indicated.
- ellipsoidal algorithm;
- interior point algorithm;
- convergence robustness;
- maximal violated constraint;
- bounding box;