A new neural network for convex quadratic minimax problems with box and equality constraints

This paper presents a new neural network for solving a class of convex quadratic minimax problems with equality and box constraints by means of the sufficient and necessary conditions of the saddle point of the underlying function. By defining a proper energy function, the proposed model is proved to be stable in the sense of Lyapunov and converges to an exact solution of the original problem for any starting point under the condition that the objective function is convex-concave on the linear equation sets. Compared with the existing neural networks for the same convex quadratic minimax problem, the proposed neural network has the fewest neurons and lower complexity, and requires weaker stability conditions. The validity and transient behavior of the proposed neural network are demonstrated by some numerical results.