Skip to main content
SpringerLink
Log in

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

  • Conference paper
Book cover Theory and Applications of Models of Computation (TAMC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7287))

  • 1077 Accesses

Abstract

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

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bland, R.G., Goldfarb, D., Todd, M.J.: The ellipsoid method: A Survey. Operations Research 29, 1039–1091 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  2. Buck, R.C.: Partion of space. The American Mathematical Monthly 50, 541–544 (1943)

    Article  MathSciNet  MATH  Google Scholar 

  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), http://nb.vse.cz/~cernym/plr.pdf

  4. Dyer, M., Gritzmann, P., Hufnagel, A.: On the complexity of computing mixed volumes. SIAM Journal on Computing 27, 356–400 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  5. Goffin, J.-L.: Variable metric relaxation methods. Part II: The ellipsoid method. Mathematical Programming 30, 147–162 (1984)

    MathSciNet  MATH  Google Scholar 

  6. Grötschel, M., Lovász, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimization. Springer, Heidelberg (1993)

    Book  MATH  Google Scholar 

  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. Schön, S., Kutterer, H.: Using zonotopes for overestimation-free interval least-squares — some geodetic applications. Reliable Computing 11, 137–155 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Schrijver, A.: Theory of Linear and Integer Programming. Wiley, New York (2000)

    Google Scholar 

  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. Ziegler, G.: Lectures on Polytopes. Springer, Heidelberg (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Informatics and Statistics, University of Economics, Prague, Náměstí Winstona Churchilla 4, CZ13067, Prague 3, Czech Republic

    Michal Černý & Miroslav Rada

Authors
  1. Michal Černý
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Miroslav Rada
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Resource Planning and Generation, Indian Institute of Technology Kanpur, 208016, Kanpur, India

    Manindra Agrawal

  2. Department of Pure Mathematics, Leeds, University of Leeds, LS2 9JT, UK

    S. Barry Cooper

  3. Institute of Software, Chinese Academy of Sciences, P.O. Box 8718, 100190, Beijing, P.R. China

    Angsheng Li

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Černý, M., Rada, M. (2012). Polynomial Time Construction of Ellipsoidal Approximations of Zonotopes Given by Generator Descriptions. In: Agrawal, M., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2012. Lecture Notes in Computer Science, vol 7287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29952-0_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-29952-0_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29951-3

  • Online ISBN: 978-3-642-29952-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation