Abstarct: Semidefinite problems has been very much considered in recent decades and includes a very large area of convex optimization problems. Many of the important issues in system theory and control, structural optimization, statistics, and other fields can be formulated as a Semidefinite problem. So far, there are several ways to solve a Semidefinite problems. However, the use of neural networks to solve this problem has not been reported except in a small number. In this thesis, two neural network models will be presented to solve a semidefinite programming problem. We will show that the proposed equilibrium point of the neural network and the optimal solution of the semidefinite problem are equivalent. The stability and convergence of the proposed neural network models will also be proved. Also, for the first time, we present a neural network model for solving a nonlinear semidefinite problem. The stability and global convergence prove to be the optimal solution of the main problem. By providing examples we confirm the theoretical results.