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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.Keywords Parametric convex discrete optimal control problem · Optimal value function · Subdifferentials · Linear operator with closed range · Adjoint operator. Mathematics Subject Classification (2000)

As a complement to two recent papers by An and Yen [2], and by An and Yao [1] on subdifferentials of the optimal value function of infinite-dimensional convex optimization problems, this paper studies the differential stability of convex optimization problems, where the solution set may be empty. By using a suitable sum rule for ε-subdifferentials, we obtain exact formulas for computing the ε-subdifferential of the optimal value function. Several illustrative examples are also given.