A CONVERGENCE ANALYSIS FOR AN ALGORITHM COMPUTING A SYMMETRIC LOW RANK ORTHOGONAL APPROXIMATION OF A SYMMETRIC TENSOR

摘要

In this paper, we present an algorithm for solving the problem of the symmetric low rank orthogonal tensor approximation for a given symmetric tensor. Proximality technique and shifted power technique are tailored into this algorithm. Interestingly, we can show that this algorithm converges globally without any assumption once the parameters are chosen appropriately, and moreover the convergence rate is sublinear with an explicitly given rate and it is better than the usual O(1/p) of first order methods in optimization.