Algorithm Research On Tensor Eigenvalue Complementation Problem

Tensor eigenvalue complementarity problem is a special class of complementarity problems based on complementarity problems and tensor eigenvalue problems.With the development and application of complementarity problems and tensor eigenvalue problems,the research on tensor eigenvalue complementarity problems also has rich achievements.We mainly study the algorithms for solving different kinds of tensor eigenvalue complementarity problems.The thesis consists of three chapters and the main research contents are summarized as follows:In the first chapter,the basic situation of eigenvalue complementarity problems,tensor eigenvalue problems and tensor eigenvalue complementarity problems is introduced.We also give the basic structures of tensor eigenvalue complementarity problems with different forms.In the second chapter,we study the tensor quadratic eigenvalue complementarity problem.We give the existence theorem of the solutions for tensor quadratic eigenvalue complementarity problem.By constructing auxiliary variables,we propose the equivalence relation between tensor quadratic eigenvalue complementarity problem and corresponding tensor generalized eigenvalue complementarity problems.Under the condition of the existence of solutions,tensor quadratic eigenvalue complementarity problem is equivalently transformed into the unconstrained optimization problem.The semi-smooth Newton method with global convergence is given.The numerical experiments show that the method is effective for solving tensor quadratic eigenvalue complementarity problem.In the third chapter,we study tensor eigenvalue complementarity problems with different structures.By using the Fischer-Burmeister function,we transform different tensor eigenvalue complementarity problems into unconstrained optimization problems.We present a modified spectral PRP conjugate gradient method with Armijo line search for solving tensor eigenvalue complementarity problems and prove the global convergence analysis of the method under the general assumptions.The final numerical results show the validity of the given method for solving tensor eigenvalue complementarity problems.