In this paper we propose an efficient method for solving the spherically constrained
homogeneous polynomial optimization problem. The new approach has the following three …

Understanding exotic forms of magnetism in quantum spin systems is an emergent topic of
modern condensed matter physics. Quantum dynamics can be described by particle-like …

This paper studies the so-called biquadratic optimization over unit spheres
x∈R^n,y∈R^m1≦i,k≦n,\,1≦j,l≦mb_ijklx_iy_jx_ky_l, subject to ‖x‖=1, ‖y‖=1. We …

In this paper, we consider approximation algorithms for optimizing a generic multi-variate
homogeneous polynomial function, subject to homogeneous quadratic constraints. Such …

In this paper, we consider a bi‐quadratic homogeneous polynomial optimization problem
over two unit spheres arising in nonlinear elastic material analysis and in entanglement …

We study geometrical aspects of entanglement, with the Hilbert–Schmidt norm defining the
metric on the set of density matrices. We focus first on the simplest case of two two-level …

In this paper we define the best rank-one approximation ratio of a tensor space. It turns out
that in the finite dimensional case this provides an upper bound for the quotient of the …

Real rectangular tensors arise from the strong ellipticity condition problem in solid
mechanics and the entanglement problem in quantum physics. In this paper, we …

In this paper, we study the convergence property of a block improvement method (BIM) for
the bi‐quadratic polynomial optimization problem over unit spheres. We establish the global …

Tensor learning is a powerful tool for big data analytics and machine learning, eg, gene
analysis and deep learning. However, tensor learning algorithms are compute-intensive …