A FAST CONTINUOUS METHOD FOR THE EXTREME EIGENVALUE PROBLEM

作者：Gao, Huan; Li, Zhibao^*; Zhang, Haibin

来源：Journal of Industrial and Management Optimization, 2017, 13(3): 1587-1599.

DOI：10.3934/jimo.2017008

• Eigenvalue
• continuous method
• dynamic system
• self-adaptive strategy

Matrix eigenvalue problems play a significant role in many areas of computational science and engineering. In this paper, we propose a fast continuous method for the extreme eigenvalue problem. We first convert such a nonconvex optimization problem into a minimization problem with concave objective function and convex constraints based on the continuous methods developed by Golub and Liao. Then, we propose a continuous method for solving such a minimization problem. To accelerate the convergence of this method, a self-adaptive step length strategy is adopted. Under mild conditions, we prove the global convergence of this method. Some preliminary numerical results are presented to verify the effectiveness of the proposed method eventually.

• 出版日期2017-7
• 单位北京工业大学; 中南大学