A discrete optimal control problem

A certain class of discrete optimization problems is investigated using the framework of nonlinear programming. It is shown that a discrete maximum principle similar to the Pontryagin maximum principle is valid for a subclass of these problems, specifically systems with linear dynamics, convex inequality constraints and convex performance criteria. This result extends the applicability of the discrete maximum principle to a class of problems not covered by the Rozonoer-Halkin formulation.