Quadratic tensor eigenvalue complementarity problems

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