Tractable Relaxations for the Cubic One-Spherical Optimization Problem
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.
KeywordsCubic 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.