Global convergence analysis on projection-type neural networks

Projection-type neural networks for optimization problems can naturally guarantee the feasibility of solutions, and they have advantages over other networks for their less parameters, low searching space dimension and simple structure. But only for strict convex quadratic optimization with bound constraints, their global convergence has been proved theoretically. In this paper, the global convergence of such networks for general convex programming problem is proved by means of ordinary differential equation theory and LaSalle invariance principal. At the same time, their exponential convergent speed is discussed. The obtained results settle the applicability of the networks. Several numerical examples are given to demonstrate the feasibility and efficiency of the networks.