An Adaptive Trust-Region Method for Generalized Eigenvalues of Symmetric Tensors (Journal of Computational Mathematics, 2021)
For symmetric tensors, computing generalized eigenvalues is equivalent to a homogenouspolynomial optimization over the unit sphere. In this paper, we present an adaptive trust-region method for generalized eigenvalues of symmetric tensors. One of the features isthat the trust-region radius is automatically updated by the adaptive technique to improvethe algorithm performance. The other one is that a projection scheme is used to ensurethe feasibility of all iteratives. Global convergence and local quadratic convergence ofour algorithm are established, respectively. The preliminary numerical results show theefficiency of the proposed algorithm.
Keywords: Symmetric tensors; Generalized eigenvalues; Trust-region; Global convergence; Local quadratic convergence.