A recurrent neural network for convex inequality constrained optimization problems is proposed, based on the logarithmic barrier function with a time varying barrier parameter. Strictly feasible interior point trajectories are created by the network which converge to the exact solution of the constrained problem as t/spl rarr//spl infin/. A strictly feasible initial point is required; two methods for obtaining such points are presented. Numerical results show that the method is efficient and accurate.