In this letter, we propose a rank-one tensor updating algorithm for solving tensor completion
problems. Unlike the existing methods which penalize the tensor by using the sum of …

Polynomial optimization have been a hot research topic for the past few years and its
applications range from Operations Research, biomedical engineering, investment science …

This paper presents a generalization of the spectral norm and the nuclear norm of a tensor
via arbitrary tensor partitions, a much richer concept than block tensors. We show that the …

The recent decade has witnessed a surge of research in modelling and computing from two-
way data (matrices) to multiway data (tensors). However, there is a drastic phase transition …

It is known that computing the spectral norm and the nuclear norm of a tensor is NP-hard in
general. In this paper, we provide neat bounds for the spectral norm and the nuclear norm of …

This paper studies models and algorithms for a class of tensor optimization problems, based
on a rank-1 equivalence property between a tensor and certain unfoldings. It is first shown …

We study two instances of polynomial optimization problem over a single sphere. The first
problem is to compute the best rank-1 tensor approximation. We show the equivalence …

The matrix spectral norm and nuclear norm appear in enormous applications. The
generalization of these norms to higher-order tensors is becoming increasingly important …

Complex polynomial optimization problems arise from real-life applications including radar
code design, MIMO beamforming, and quantum mechanics. In this paper, we study complex …

In this paper, we establish hardness and approximation results for various Lp-ball
constrained homogeneous polynomial optimization problems, where p∈[2,∞]. Specifically …