Differential Stability in a Multi-Objective Optimal Control Problems with a Possibly Empty Solution Set

This paper studies the first-order behavior of the weak optimal value mapping in a parametric multi-objective discrete optimal control problem under linear state equations, where the solution set may be empty. By establishing an abstract result on the \(\varepsilon \)-weak subdifferential of the weak optimal value mapping in a parametric multi-objective mathematical programming problem with an inclusion constraint, we derive a formula for computing the \(\varepsilon \)-weak subdifferential of the weak optimal value mapping in a parametric multi-objective discrete optimal control problem. The obtained results are proved directly without using scalarization techniques.