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.
Similar content being viewed by others
Notes
See D’Ambrosio et al. [1].
References
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
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)
Du, D., Hu, X.: Steiner Tree Problems in Computer Communication Networks. World Scientific, Hackensack (2008)
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)
Garey, M., Graham, R., Johnson, D.: The complexity of computing Steiner minimal trees. SIAM J. Appl. Math. 32, 835–859 (1977)
Hwang, F., Richards, D., Winter, W.: The Steiner Tree Problem. Ann. Disc. Math., vol. 53. Elsevier, Amsterdam (1992)
Lee, J., Skipper, D.: Virtuous smoothing for global optimization. J. Global Optim. 69(3), 677–697 (2017)
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)
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)
Xu, L., Lee, J., Skipper, D.: More virtuous smoothing. Technical report (2018). arXiv:1802.09112
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
Corresponding author
Rights and permissions
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11590-018-1295-1