A variational approach to the discrete maximum principle

In this paper, the nondifferentiable optimal control problem with discrete time is considered. For this problem, the discrete maximum principle is derived under weak assumptions concerning the performance index and inequality constraints. The technique of the proof is also used to formulate a globaily convergent algorithm based on the discrete maximum principle. At every iteration of this algorithm, a convex optimal control problem must be solved. An efficient version of a proximity algorithm is proposed for this convex problem.