Subgradients of the Value Function in a Parametric Convex Optimal Control Problem

Differential Stability of a Class of Convex Optimal Control Problems

“…Namely, based on the paper of An and Toan [1] about differential stability of parametric convex mathematical programming problems, we will get new results on computing the subdifferential and the singular subdifferential of the optimal value function. Among other things, our result on computing the subdifferential extends and improves the main result of [21]. Moreover, we also describe in details the process of finding vectors belonging to the subdifferential (resp., the singular subdifferential) of the optimal value function.…”

“…Hence According to the condition v ∈ ker Ψ A , we have The assumption (H 3 ) in [21] can be stated as follows Proof. By (A5) and the definition of Ψ C , for any v ∈ L q ([0, 1], R n ), one has 1].…”

“…Very recently, Thuy and Toan [21] have obtained a formula for computing the subdifferential of the optimal value function to a parametric unconstrained convex optimal control problem with a convex objective function and linear state equations.…”

“…The aim of this paper is to develop the approach of [21] to deal with constrained control problems. Namely, based on the paper of An and Toan [1] about differential stability of parametric convex mathematical programming problems, we will get new results on computing the subdifferential and the singular subdifferential of the optimal value function.…”

Generalized Clarke epiderivatives of the extremum multifunction to a multi-objective parametric discrete optimal control problem

“…Problems of this type are studied in [1,4,7,17,18,28,39,40,45] and the references therein. Multiobjective optimal control is an essential branch of optimal control theory.…”