Abstract
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.
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Acknowledgments
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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Buchheim, C., Fampa, M., Sarmiento, O. (2020). Tractable Relaxations for the Cubic One-Spherical Optimization Problem. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_28
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DOI: https://doi.org/10.1007/978-3-030-21803-4_28
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