A projection neural network and its application to constrained optimization problems

In this paper, we present a recurrent neural network for solving the nonlinear projection formulation. It is shown here that the proposed neural network is stable in the sense of Lyapunov and globally convergent, globally asymptotically stable, and globally exponentially stable, respectively under different conditions. Compared with the existing neural network for solving the projection formulation, the proposed neural network has a single-layer structure and is amenable to parallel implementation. Moreover, the proposed neural network has no Lipschitz condition, and, thus can be applied to solve a very broad class of constrained optimization problems that are special cases of the nonlinear projection formulation. Simulation shows that the proposed neural network is effective in solving these constrained optimization problems.