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A Novel Neural Network for a Class of Convex Quadratic Minimax Problems

xinbaog{at}snnu.edu.cn College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, China

Li-Zhi Liao

liliao{at}hkbu.edu.hk Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China

Based on the inherent properties of convex quadratic minimax problems, this article presents a new neural network model for a class of convex quadratic minimax problems. We show that the new model is stable in the sense of Lyapunov and will converge to an exact saddle point in finite time by defining a proper convex energy function. Furthermore, global exponential stability of the new model is shown under mild conditions. Compared with the existing neural networks for the convex quadratic minimax problem, the proposed neural network has finite-time convergence, a simpler structure, and lower complexity. Thus, the proposed neural network is more suitable for parallel implementation by using simple hardware units. The validity and transient behavior of the proposed neural network are illustrated by some simulation results.