A minimax method for finding saddle critical points of upper semi-differentiable locally Lipschitz continuous functional in Hilbert space and its convergence
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Abstract:
A minimax characterization for finding nonsmooth saddle critical points, i.e., saddle critical points of locally Lipschitz continuous functional, in Banach space is presented in [X. Yao and J. Zhou, A local minimax characterization for computing multiple nonsmooth saddle critical points, Math. Program., 104 (2005), no. 2-3, Ser. B, 749-760]. By this characterization, a descent-max method is devised. But, there is no numerical experiment and convergence result for the method. In this paper, to a class of locally Lipschitz continuous functionals, a minimax method for computing nonsmooth saddle critical points in Hilbert space will be designed. Numerical experiments will be carried out and convergence results will be established.References
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Additional Information
- Xudong Yao
- Affiliation: Department of Mathematic, Shanghai Normal University, Shanghai, China 200234
- Email: xdyao@shnu.edu.cn
- Received by editor(s): July 23, 2010
- Received by editor(s) in revised form: October 23, 2011
- Published electronically: March 28, 2013
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 82 (2013), 2087-2136
- MSC (2010): Primary 65K10, 65K15, 65N12; Secondary 49M37
- DOI: https://doi.org/10.1090/S0025-5718-2013-02669-5
- MathSciNet review: 3073193