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This paper presents a one-layer recurrent neural network for solving convex programming problems subject to linear equality and nonnegativity constraints. The number of neurons in the neural network is equal to that of decision variables in the optimization problem. Compared with the existing neural networks for optimization, the proposed neural network has lower model complexity. Moreover, the proposed neural network is proved to be globally convergent to the optimal solution(s) under some mild conditions. Simulation results show the effectiveness and performance of the proposed neural network.