Polynomial Time Construction of Ellipsoidal Approximations of Zonotopes Given by Generator Descriptions

  • Michal Černý
  • Miroslav Rada
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7287)


We adapt Goffin’s Algorithm for construction of the Löwner-John ellipsoid for a full-dimensional zonotope given by the generator description.


Unit Ball Generator Description Ellipsoid Method Ellipsoidal Approximation Facet Description 
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  1. 1.
    Bland, R.G., Goldfarb, D., Todd, M.J.: The ellipsoid method: A Survey. Operations Research 29, 1039–1091 (1981)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Buck, R.C.: Partion of space. The American Mathematical Monthly 50, 541–544 (1943)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Černý, M., Antoch, J., Hladík, M.: On the possibilistic approach to linear regression models involving uncertain, indeterminate or interval data. Technical Report, Department of Econometrics, University of Economics, Prague (2011),
  4. 4.
    Dyer, M., Gritzmann, P., Hufnagel, A.: On the complexity of computing mixed volumes. SIAM Journal on Computing 27, 356–400 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Goffin, J.-L.: Variable metric relaxation methods. Part II: The ellipsoid method. Mathematical Programming 30, 147–162 (1984)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Grötschel, M., Lovász, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimization. Springer, Heidelberg (1993)zbMATHCrossRefGoogle Scholar
  7. 7.
    Guibas, L.J., Nguyen, A., Zhang, L.: Zonotopes as bounding volumes. In: Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 803–812. SIAM, Pennsylvania (2003)Google Scholar
  8. 8.
    Schön, S., Kutterer, H.: Using zonotopes for overestimation-free interval least-squares — some geodetic applications. Reliable Computing 11, 137–155 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Schrijver, A.: Theory of Linear and Integer Programming. Wiley, New York (2000)Google Scholar
  10. 10.
    Zaslavsky, T.: Facing up to arrangements: face-count formulas for partitions of space by hyperplanes. Memoirs of the American Mathematical Society 154 (1975)Google Scholar
  11. 11.
    Ziegler, G.: Lectures on Polytopes. Springer, Heidelberg (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Michal Černý
    • 1
  • Miroslav Rada
    • 1
  1. 1.Faculty of Informatics and StatisticsUniversity of Economics, PraguePrague 3Czech Republic

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