A neural network model for general minimax problem

Minimax problem is significant topic in signal process (e.g. filter design) and process control (e.g. controller design), which is relevant to robustness, parameters uncertainty, and signal noise etc. However, efficient algorithms are scarce, especially those for general minimax problem with equality and inequality nonlinear constraints. In this paper a novel neural network for general minimax problem has been constructed based on a penalty function approach. The unique request on objective function and constraint functions is that they are first-order differentiable. A Lyapunov function is established for the global stability analysis. The network is simulated and its validity is illustrated by numerical examples. Simulation results show that minimax neural network, which computes in second, is more efficient than the previous GA/SGA algorithms, which computes in minutes.