张量广义高次特征值互补问题解的一个刻划

A Characterization of Solutions of Tensor Generalized Higher-degree Eigenvalue Complementarity Problem

提出了一类张量广义高次特征值互补问题与非线性规划之间的等价关系.进一步给出了相应非线性规划问题的稳定点是张量广义高次特征值互补问题解的充要条件,最后,在特征值次数满足一定条件下,证明了张量广义高次特征值互补问题可被转化为张量高次特征值互补问题.

This paper proposes an equivalence relation between the considered tensor generalized higher-degree eigenvalue complementarity problem and nonlinear programming problems.Furthermore,a necessary and sufficient condition for the stationary point of the corresponding nonlinear programming problem being the solution of the tensor generalized higher-degree eigenvalue complementarity problem is given.Finally,under the degree of eigenvalues satisfies certain conditions,it is proved that the tensor generalized higher-degree eigenvalue complementarity problem can be transformed into the tensor higher-degree eigenvalue complementary problem.