Abstarct: Recently methods of optimization baxsed on artificial intelligence approaches have been developed remarkable success in solving optimization problems efficiently acquired. Methods such as Genetic Algorithms, Tabu Search, refrigeration simulation and neural networks, their ability to solve large problems have good action. In this thesis, we tried one model of recursive neural network is presented to solve assignment and shortest path problems. The main idea is to replace the assignment problem with a linear programming (LP) problem. According to the saddle point theorem, optimization theory, convex analysis theory, Lyapunov stability theory and LaSalle invariance principle, the equilibrium point of the proposed neural network is proved to be equivalent to the optimal solution of the original problem. It is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the assignment problem.