LIPSCHITZ CONTINUITY FOR CONSTRAINED PROCESSES

Lipschitz continuity properties are studied for ″constrained processes″ . As applications of the general theory, mathematical programs and optimal control problems are considered. It is shown that if the gradients of the binding constraints satisfy an independence condition, then the solution and the dual multipliers of a convex mathematical program are a Lipschitz continuous function of the data. Similarly, it is proved that the optimal control and the dual multipliers for strictly convex control problems with convex constraints on the state and the control are Lipschitz continuous in time.