  This paper is concerned with solving some structured multi-linear systems,
which are called tensor absolute value equations. This kind of absolute value
equations is closely related to tensor complementarity problems and is a
generalization of the well-known absolute value equations in the matrix case.
We prove that tensor absolute value equations are equivalent to some special
structured tensor complementary problems. Some sufficient conditions are given
to guarantee the existence of solutions for tensor absolute value equations. We
also propose a Levenberg-Marquardt-type algorithm for solving some given tensor
absolute value equations and preliminary numerical results are reported to
indicate the efficiency of the proposed algorithm.
