A Class Of Tensor Higher-order Eigenvalue Complementarity Problems

This thesis proposes a class of tensor higher-degree eigenvalue complementarity problems,which have closely relationship with a class of nonlinear differential inclusion problems.The equivalent connection between the considered tensor higher-degree eigenvalue complementarity problems and the corresponding homogeneous polynomial fractional programming is studied,and a result on existence of solution for tensor eigenvalue complementarity problems is proved.The eigenvalue complementarity problem for matrix which has many widely applications is a special type of complementarity problems,and also is the class of important form of the quadratic eigenvalue complementarity problem for matrix.Tensors as a natural extension of the concept of matrices,a related problem is the higher-order tensor eigenvalue complementarity problem.The eigenvalue complementarity problems for higher-order tensors are NP-complete and very difficult to solve efficiently,especially when the dimension of the problem is large.So,in this case,we studied the equivalent connection between the considered tensor higher-order eigenvalue complementarity problems and the corresponding homogeneous polynomial fractional programming.In this thesis,we first review the evolution of the eigenvalue complementarity problem for matrix,the eigenvalue problem for tensor and so on.Then,we proposes a class of tensor higher-degree eigenvalue complementarity problems.Based upon this,we get the existence of the solution of the tensor higher-order eigenvalue complementarity problems.