What Is the Multilinear Eigenvalue Problem Called?

[Manchot]

I'm trying to do something that requires solving an eigenvalue problem of the form
$$A_{imkl} c_m c_k c^*_l=\lambda c_i$$
where A is a known rank-4 tensor, $\lambda$ is the eigenvalue, and the $c_i$'s are a set of unknown coefficients that I need to determine. I would guess that this type of problem should be solvable, but I have no idea where to start. For all I know, it's a problem with a common name that I just don't know. Any pointers?

 

[Manchot]

If anyone even knew what this class of problem is called, that would be tremendously helpful. (A Google search on various terms related to "eigenvalues" comes up with a lot of useless results.)