An SDP Method for Copositivity of Partially Symmetric Tensors

Algorithm 1

An SDP method for copositivity of a partially symmetric tensor .

	Step 0: given an arbitrary vector . Let .
Step 1: solve the semidefinite relaxation (17). If , then stop, and is copositive. If , go to Step 2.
Step 2: solve the following semidefinite program:
for an optimizer if it is feasible. If it is infeasible, let and go to Step 1.
Step 3: let . If , then is not copositive and stop. Otherwise, let and go to Step 1.