Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



A minimax method for finding saddle critical points of upper semi-differentiable locally Lipschitz continuous functional in Hilbert space and its convergence

Author: Xudong Yao
Journal: Math. Comp. 82 (2013), 2087-2136
MSC (2010): Primary 65K10, 65K15, 65N12; Secondary 49M37
Published electronically: March 28, 2013
MathSciNet review: 3073193
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 65K10, 65K15, 65N12, 49M37

Retrieve articles in all journals with MSC (2010): 65K10, 65K15, 65N12, 49M37

Additional Information

Xudong Yao
Affiliation: Department of Mathematic, Shanghai Normal University, Shanghai, China 200234

Keywords: Locally Lipschitz continuous functional, nonsmooth saddle critical point, minimax method, convergence
Received by editor(s): July 23, 2010
Received by editor(s) in revised form: October 23, 2011
Published electronically: March 28, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.