2017/11/10 by Jiawang Nie, Zi Yang, Nie, Jiawang +3 · 1 citation
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1711.03704
openalex publication_date 2017/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A real symmetric matrix (resp., tensor) is said to be copositive if the associated quadratic (resp., homogeneous) form is greater than or equal to zero over the nonnegative orthant. The problem of detecting their copositivity is NP-hard. This paper proposes a complete semidefinite relaxation algorithm for detecting the copositivity of a matrix or tensor. If it is copositive, the algorithm can get a certificate for the copositivity. If it is not, the algorithm can get a point that refutes the copositivity. We show that the detection can be done by solving a finite number of semidefinite relaxations, for all matrices and tensors.