165 citations · 445 across the 26 of their papers we have counts for
5 papers · 1 filter
Quantifying low rank approximations of third order symmetric tensors
Shenglong Hu, Defeng Sun, Kim-Chuan Toh
In this paper, we present a method to certify the approximation quality of a low rank tensor to a given third order symmetric tensor. Under mild assumptions, best low rank approxim…
When geometry meets optimization theory: partially orthogonal tensors
Ke Ye, Shenglong Hu
Due to the multi-linearity of tensors, most algorithms for tensor optimization problems are designed based on the block coordinate descent method. Such algorithms are widely employ…
Linear Convergence of an Alternating Polar Decomposition Method for Low Rank Orthogonal Tensor Approximations
Shenglong Hu, Ke Ye
Low rank orthogonal tensor approximation (LROTA) is an important problem in tensor computations and their applications. A classical and widely used algorithm is the alternating pol…
Best Nonnegative Rank-One Approximations of Tensors
Shenglong Hu, Defeng Sun, Kim-Chuan Toh
In this paper, we study the polynomial optimization problem of multi-forms over the intersection of the multi-spheres and the nonnegative orthants. This class of problems is NP-har…
A Tensor Analogy of Yuan's Theorem of the Alternative and Polynomial Optimization with Sign structure
Shenglong Hu, Guoyin Li, Liqun Qi
Yuan's theorem of the alternative is an important theoretical tool in optimization, which provides a checkable certificate for the infeasibility of a strict inequality system invol…