SDP relaxation algorithms for $$\mathbf {P}(\mathbf {P}_0)$$-tensor detection

Abstract

$$\mathbf {P}$$-tensor and $$\mathbf {P}_0$$-tensor are introduced in tensor complementarity problem, which have wide applications in game theory. In this paper, we establish SDP relaxation algorithms for detecting $$\mathbf {P}(\mathbf {P}_0)$$-tensor. We first reformulate $$\mathbf {P}(\mathbf {P}_0)$$-tensor detection problem as polynomial optimization problems. Then we propose the SDP relaxation algorithms for solving the reformulated polynomial optimization problems. Numerical examples are reported to show the efficiency of the proposed algorithms.