Novel Continuous- and Discrete-Time Neural Networks for Solving Quadratic Minimax Problems With Linear Equality Constraints

This article presents two novel continuous- and discrete-time neural networks (NNs) for solving quadratic minimax problems with linear equality constraints. These two NNs are established based on the conditions of the saddle point of the underlying function. For the two NNs, a proper Lyapunov function is constructed so that they are stable in the sense of Lyapunov, and will converge to some saddle point(s) for any starting point under some mild conditions. Compared with the existing NNs for solving quadratic minimax problems, the proposed NNs require weaker stability conditions. The validity and transient behavior of the proposed models are illustrated by some simulation results.