Tractable Relaxations for the Cubic One-Spherical Optimization Problem

  • Christoph Buchheim
  • Marcia FampaEmail author
  • Orlando Sarmiento
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)


We consider the cubic one-spherical optimization problem, consisting in minimizing a homogeneous cubic function over the unit sphere. We propose different lower bounds that can be computed efficiently, using decompositions of the objective function and well-known results for the corresponding quadratic problem variant.


Cubic one-spherical optimization problem Best rank-1 tensor approximation Trust region subproblem Convex relaxation 



C. Buchheim has received funding from the European Unions Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 764759. M. Fampa was supported in part by CNPq-Brazil grants 303898/2016-0 and 434683/2018-3. O. Sarmiento contributed much of his work while visiting the Technische Universität Dortmund, Dortmund, Germany, supported by a Research Fellowship from CAPES-Brazil - Finance Code 001.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Technische Universität DortmundDortmundGermany
  2. 2.Universidade Federal do Rio de JaneiroRio de JaneiroBrazil

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