The model-order reduction techniques Proper Orthogonal Decomposition (POD) and Discrete Empirical Interpolation Method (DEIM) have been applied for the optimal control of Burgers' equation. Accuracy and performance of the reduced models have been studied in detail for different values of the viscosity parameter and different sizes of the discretization. Therefore, the three different optimization algorithms Newton-type, BFGS and SPG have been taken into account.