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

摘要

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