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

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Abstract

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.

Keywords

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

Mathematics Subject Classification (2010)

58E05 58E30 35P30 65N12 65N30 

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Notes

Acknowledgments

The author would like to thank referees for their helpful comments.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Normal UniversityShanghaiChina

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