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Differential Stability in a Multi-Objective Optimal Control Problems with a Possibly Empty Solution Set
N. T. Toan
,
L. Q. Thuy
Abstract
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.