Skip to main content
SpringerLink
Log in

On a nonconvex MINLP formulation of the Euclidean Steiner tree problem in n-space: missing proofs

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

We supply proofs for a few key results concerning smoothing square roots and model strengthening for a mixed-integer nonlinear-optimization formulation of the the Euclidean Steiner tree problem.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. See D’Ambrosio et al. [1].

References

  1. D’Ambrosio, C., Fampa, M., Lee, J., Vigerske, S.: On a nonconvex MINLP formulation of the Euclidean Steiner tree problem in \(n\)-space. Technical report, Optimization Online (2014). http://www.optimization-online.org/DB_HTML/2014/09/4528.html

  2. D’Ambrosio, C., Fampa, M., Lee, J., Vigerske, S.: On a nonconvex MINLP formulation of the Euclidean Steiner Tree Problem in n-space. In: Bampis, E. (ed.) Experimental Algorithms, LNCS, vol. 9125. Springer, pp. 122–133 (2015)

  3. Du, D., Hu, X.: Steiner Tree Problems in Computer Communication Networks. World Scientific, Hackensack (2008)

    Book  Google Scholar 

  4. Fampa, M., Lee, J., Maculan, N.: An overview of exact algorithms for the Euclidean Steiner tree problem in \(n\)-space. Int. Trans. Oper. Res. 23(5), 861–874 (2016)

    Article  MathSciNet  Google Scholar 

  5. Garey, M., Graham, R., Johnson, D.: The complexity of computing Steiner minimal trees. SIAM J. Appl. Math. 32, 835–859 (1977)

    Article  MathSciNet  Google Scholar 

  6. Hwang, F., Richards, D., Winter, W.: The Steiner Tree Problem. Ann. Disc. Math., vol. 53. Elsevier, Amsterdam (1992)

    Google Scholar 

  7. Lee, J., Skipper, D.: Virtuous smoothing for global optimization. J. Global Optim. 69(3), 677–697 (2017)

    Article  MathSciNet  Google Scholar 

  8. Maculan, N., Michelon, P., Xavier, A.: The Euclidean Steiner tree problem in \({R}^n\): a mathematical programming formulation. Ann. OR 96(1–4), 209–220 (2000)

    Article  Google Scholar 

  9. Wächter, A., Biegler, L.: On the implementation of an interior-point filter line-search algorithm for large-scale NLP. Math. Prog. 106, 25–57 (2006)

    Article  Google Scholar 

  10. Xu, L., Lee, J., Skipper, D.: More virtuous smoothing. Technical report (2018). arXiv:1802.09112

Download references

Acknowledgements

J. Lee was partially supported by NSF Grant CMMI-1160915 and ONR Grant N00014-14-1-0315, and Laboratoire d’Informatique de l’École Polytechnique. M. Fampa was partially supported by CNPq and FAPERJ.

Author information

Authors and Affiliations

  1. LIX CNRS (UMR7161), École Polytechnique, 91128, Palaiseau Cedex, France

    Claudia D’Ambrosio

  2. Instituto de Matemática and COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil

    Marcia Fampa

  3. IOE Department, University of Michigan, Ann Arbor, MI, USA

    Jon Lee

  4. ZIB (Konrad-Zuse-Zentrum für Informationstechnik Berlin), Berlin, Germany

    Stefan Vigerske

Authors
  1. Claudia D’Ambrosio
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marcia Fampa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jon Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Stefan Vigerske
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jon Lee.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

D’Ambrosio, C., Fampa, M., Lee, J. et al. On a nonconvex MINLP formulation of the Euclidean Steiner tree problem in n-space: missing proofs. Optim Lett 14, 409–415 (2020). https://doi.org/10.1007/s11590-018-1295-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-018-1295-1

Keywords

Search

Navigation