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

Abstract

P-tensor and 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 P(P 0 )-tensor. We first reformulate P(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.

Semidefinite relaxation method for polynomial optimization with second-order cone complementarity constraints

“…Step 2: Solve the kth-order SDP relaxation (20). If it is infeasible, then SOCPOPCC is infeasible and stop.…”

“…By exploring solution properties, such problems are equivalently reformulated as polynomial optimization problems and SDP relaxation methods can be applied to solve the problems. By this way, SDP relaxation methods are applied to tensor eigenvalue complementarity problem [5] and [6], P(P 0 )-tensor detection [20], copositive tensor detection [13,19] and so on.…”

A semidefinite relaxation method for second-order cone polynomial complementarity problems

“…Tensor eigenvalue complementarity problems can be solved by SDP relaxation methods [8,10]. Copositivity and P-property can be checked by SDP relaxation methods in [24,30]. Motivated by these, we consider an interesting question: can we apply SDP relaxation methods to solve the second-order cone tensor complementarity problem?…”