Theoretical Analysis Of Solution Sets Of Tensor Complementarity Problems

Tensor theory analysis and calculation is an important branch of numerical algebra.It is also closely related to multilinear algebra.It has important applications in signal processing,quantum mechanics and medical imaging.In this thesis,we mainly analyze copositive tensor complementarity problem and tensor polynomial complementarity problem.In Chapter 1,we mainly introduce the research background and current situation of complementary problem,copositive matrix complementarity problem and polynomial complementarity problem.In Chapter 2,we first give some basic symbols that are relevant to this thesis,then the concepts of(strictly)copositive tensor,(strictly)positive definite tensor,(strictly)semipositive tensor and(strictly)positive definite tensor are reviewed,which makes necessary preparation for the following research.In Chapter 3,we mainly study the copositive tensor complementarity problem.Firstly,the related concepts and basic forms of copositive tensor complementarity problems are given,which provide an important theoretical basis for the subsequent discussion of the exceptional family and solvability of copositive tensor complementarity problems.Secondly,with the help of topological degree theory and the concept of exceptional family,the problem of copositive tensor complementarity can be solved or exceptional family exist.Finally,it is further proved that under the conditions of Isac-Carbone's,Karamardian's,pseudomonotone and weakly proper,there must be a solution to the problem of copositive tensor complementarity.In Chapter 4,we mainly study the tensor polynomial complementarity problem.This chapter is divided into two sections.The first section introduces the concept of tensor polynomial complementarity problem and the concrete form of tensor polynomial complementarity problem.In the second section,we study the error bound estimation of tensor polynomial complementarity problem.In Chapter 5,we made a summary of this thesis,pointed out the shortcomings of this thesis,and further clarified the future research direction.