2015/02/08 by Yisheng Song, Liqun Qi, Song, Yisheng +1
Computer Science · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Tensor decomposition and applications #math.OC
paper · pdf · doi:10.48550/arxiv.1502.02209
arxiv created 2015/02/08 · openalex publication_date 2015/02/08 · arxiv updated 2015/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The tensor complementarity problem (\q, A) is to find \x ∈ ℝn such that \x ≥ \0, \q + A\xm-1 ≥ \0, and \x^\top (\q + A\xm-1) = 0. We prove that a real tensor A is a (strictly) semi-positive tensor if and only if the tensor complementarity problem (\q, A) has a unique solution for \q>\0 (\q≥\0), and a symmetric real tensor is a (strictly) semi-positive tensor if and only if it is (strictly) copositive. That is, for a strictly copositive symmetric tensor A, the tensor complementarity problem (\q, A) has a solution for all \q ∈ ℝn.