A Ljusternik-Schnirelman minimax algorithm for finding equality constrained saddle points and its application for solving eigen problems: part I. Algorithm and global convergence

作者：Yao, Xudong^*

来源：Advances in Computational Mathematics, 2019, 45(1): 269-310.

DOI：10.1007/s10444-018-9616-6

• Ljusternik-Schnirelman critical point theory
• Ljusternik-Schnirelman minimax algorithm
• Equality constrained saddle point
• Eigen problem
• Global convergence

In Yao (J. Sci. Comput. 66, 19-40 2016), two Ljusternik-Schnirelman minimax algorithms for capturing multiple free saddle points are developed from well-known Ljusternik-Schnirelman critical point theory, numerical experiment is carried out and global convergence is established. In this paper, a Ljusternik-Schnirelman minimax algorithm for calculating multiple equality constrained saddle points is presented. The algorithm is applied to numerically solve eigen problems. Finally, global convergence for the algorithm is verified.

• 出版日期2019-2
• 单位上海师范大学