Solve Discrete Linear-Quadratic Optimal Control Problem By Alternating Direction Method

Under the assumption that the system is fully controllable, we consider a discrete linear-quadratic optimal control problem. The objective function of this problem has a completely separable structure, it can be converted to variational inequality problem with separable structure. The alternat-ing direction method is an effective method for variational inequalities. We present an inexact proximal alternating direction method for the discrete linear-quadratic optimal control problem. Comparing with other methods of solving the discrete linear quadratic optimal control problem, the alter-nating direction method can make full use of the separable structure and reduce the dimension of the problem. The numerical experiment results show that the performance is good.