| 中文摘要 | 第1-6页 |
| Abstract | 第6-10页 |
| Chapter 1 Introduction | 第10-26页 |
| ·Eigenvalues of tensors | 第10-13页 |
| ·Related polynomial optimization problems | 第13-15页 |
| ·Applications | 第15-17页 |
| ·Properties and algorithms | 第17-21页 |
| ·Main contributions and organization of this thesis | 第21-23页 |
| ·Notations | 第23-26页 |
| Chapter 2 Properties and Algorithms of H-eigenvalues of Nonnega-tive Square Tensors | 第26-58页 |
| ·Introduction | 第26-27页 |
| ·Nonnegative irreducible tensors and a simple determination rule for nonnegative irreducible tensors | 第27-29页 |
| ·Some conclusions concerning the eigenvalue of a nonnegative tensor | 第29-34页 |
| ·Geometric simplicity of the spectral radius of nonnegative irreducible tensors | 第34-41页 |
| ·The stochastic tensor and the nonnegative irreducible tensor | 第41-44页 |
| ·Polynomial-time algorithm for computing the spectral radius | 第44-47页 |
| ·Numerical results | 第47页 |
| ·Weak irreducibility and some properties for nonnegative weakly irre-ducible tensors | 第47-58页 |
| Chapter 3 Properties and Algorithms of H-singular Values of Nonneg-ative Rectangular Tensors | 第58-74页 |
| ·Introduction | 第58-59页 |
| ·Preliminaries | 第59页 |
| ·Some conclusions concerning the singular value of a nonnegative rect-angular tensor | 第59-69页 |
| ·Primitivity and the convergence of a method for finding the largest singular value of a nonnegative rectangular tensor | 第69-71页 |
| ·Polynomial-time algorithm for computing the largest singular value of a nonnegative rectangular tensor and numerical results | 第71-74页 |
| Chapter 4 Properties and Algorithms of A Reformulation for the Z-eigenvalue Problem of A Supersymmetric Tensor | 第74-104页 |
| ·Introduction | 第74-75页 |
| ·The reformulation problem and the no duality gap result | 第75-81页 |
| ·Relaxations and algorithms | 第81-96页 |
| ·Numerical results | 第96-104页 |
| Chapter 5 Solving Biquadratic Optimization Problems via Semidefi-nite Relaxation | 第104-126页 |
| ·Introduction | 第104-105页 |
| ·Semidefinite relaxations and approximate bounds | 第105-111页 |
| ·Approximation algorithms for the biquadratic optimization problems | 第111-122页 |
| ·Numerical results | 第122-126页 |
| Chapter 6 Approximation Algorithms for Trilinear Optimization With Nonconvex Constraints and Extensions | 第126-152页 |
| ·Introduction | 第126-129页 |
| ·A powerful approach to solve the trilinear optimization problem over unit spheres | 第129-134页 |
| ·Quadratic constraints | 第134-142页 |
| ·A special case | 第142-148页 |
| ·Extending to the biquadratic case | 第148-152页 |
| Chapter 7 Conclusions | 第152-154页 |
| References | 第154-164页 |
| 致谢 | 第164-166页 |
| 个人简历 | 第166-167页 |
