A FEASIBLE TRUST-REGION METHOD FOR CALCULATING EXTREME Z-EIGENVALUES OF SYMMETRIC TENSORS

作者：Hao, Chun-Lin^*; Cui, Chun-Feng; Dai, Yu-Hong

来源：Pacific Journal of Optimization, 2015, 11(2): 291-307.

• symmetric tensor
• extreme Z-eigenvalue
• feasible trust-region
• global convergence
• local quadratic convergence

It is known that computing the largest (smallest) Z-eigenvalue of a symmetric tensor is equivalent to maximizing (minimizing) a homogenous polynomial over the unit sphere. Based on such a reformulation, we shall propose a feasible trust-region method for calculating extreme Z-eigenvalues of symmetric tensors. One basic feature of the method is that the true Hessian, which is ready for polynomials, is utilized in the trust-region subproblem so that any cluster point of the iterations can be shown to satisfy the second-order necessary conditions. The other feature is that after a trial step d(k) is provided by solving the trust-region subproblem at the current point x(k), the projection of x(k) + d(k) to the unit sphere, instead of the point x(k) + d(k) itself, is judged and if successful, is used for the next point. Global convergence and local quadratic convergence of the feasible trust-region method are established for the tensor Z-eigenvalue problem. The preliminary numerical results over several testing problems show that the feasible trust-region method is quite promising.

• 出版日期2015-4
• 单位北京工业大学; 中国科学院数学与系统科学研究院