Tensor absolute value equations
For researchers in multi-linear algebra and optimization, this work extends absolute value equations to tensors, but the results are incremental as they follow known matrix-case patterns.
This paper introduces tensor absolute value equations as a generalization of matrix absolute value equations, proves their equivalence to tensor complementarity problems, provides sufficient conditions for solution existence, and proposes a Levenberg-Marquardt-type algorithm with numerical results showing efficiency.
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.