Quadratic tensor eigenvalue complementarity problems

Abstract

In this paper, we study the quadratic tensor eigenvalue complementarity problem (QTEiCP). By a randomization process, the quadratic complementarity(QC) eigenvalues are classified into two cases. For each case, the QTEiCP is formulated as an equivalent generalized moment problem. The QC eigenvectors can be computed in order. Each of them can be solved by a sequence of semidefinite relaxations. We prove that such a sequence converges in finitely many steps for generic tensors.