Abstarct: A new neural network is proposed in this thesis for solving quadratic programming problems with equality and inequality constraints. Comparing with the existing neural networks for solving such problems, the proposed neural network has fewer neurons and an one-laxyer architecture. the optimization techniques for solving pseudoconvex optimization problems are investigated. A simplified recurrent neural network is proposed according to the optimization problem. We prove that the optimal solution of the optimization problem is just the equilibrium point of the neural network, and vice versa if the equilibrium point satisfies the linear constraints. The proposed neural network is proven to be globally stable in the sense of Lyapunov and convergent to an exact optimal solution of the optimization problem. A numerical simulation is given to illustrate the global convergence of the neural network. Applications in business and chemistry are given to demonstrate the effectiveness of the neural network.