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

In 2005, a minimax characterization for nonsmooth saddle points in Banach spaces was presented by Yao and Zhou. According to this characterization, a descent-max method was devised. But, there was no numerical experiment and convergence result for the method. In this paper, to a class of locally Lipschitz continuous functionals, a new minimax method is designed. Numerical experiment is carried out and convergence results are established. This method extends two minimax methods given by Yao and Zhou in 2005 and Yao in 2013.