A Neurodynamic Approach for a Class of Convex-concave Minimax Problems

Abstract

This paper presents a neurodynamic approach for a class of convex-concave minimax problems. First, variational inequalities are given, serving as the necessary and sufficient conditions for the desired saddle point of the underlying objective function. Next, based on the variational inequalities, a neurodynamic approach is designed for the minimax problems. Taking advantage of a proper Lyapunov function, the stability of the state solution of the proposed neurodynamic approach is guaranteed. Furthermore, the proposed neurodynamic approach is able to solve the non-quadratic convex-concave minimax problem exponentially. Compared with the existing researches for the quadratic minimax problem, the proposed neurodynamic approach has wider scope of applications to some extent. Finally, a numerical experiment is provided to show the effectiveness of the proposed neurodynamic approach.