Differential Stability of Convex Discrete Optimal Control Problems

Abstract

Differential stability of convex discrete optimal control problems in Banach spaces is studied in this paper. By using some recent results of An and Yen [Appl. Anal. 94, 108--128 (2015)] on differential stability of parametric convex optimization problems under inclusion constraints, we obtain an upper estimate for the subdifferential of the optimal value function of a parametric convex discrete optimal control problem, where the objective function may be nondifferentiable. If the objective function is differentiable, the obtained upper estimate becomes an equality. It is shown that the singular subdifferential of the just mentioned optimal value function always consists of the origin of the dual space.