S-Derivative of the Extremum Multifunction to a Multi-objective Parametric Discrete Optimal Control Problem

In this paper, we derive formulae for computing the S-derivative of the extremum multifunction in a multi-objective parametric discrete optimal control problem with nonconvex objective functions and control constraints. Particularly, we obtain formulae for upper and lower evaluation on the S-derivative of the extremum multifunction via the solution of state equations, the tangent cone to the constraint sets, and the Frechet derivative of the objective functions. By establishing an abstract result on the S-derivative of the extremum multifunction in a multi-objective parametric mathematical programming problem, we derive formulae for upper and lower evaluation on the S-derivative of the extremum multifunction in a multi-objective parametric discrete optimal control problem.

Automated summary

This paper studies the computation of the S-derivative of the extremum multifunction in a multi-objective parametric discrete optimal control problem with nonconvex objective functions and control constraints. Formulae for the upper and lower evaluation on the S-derivative are obtained using the solution of state equations, the tangent cone to the constraint sets, and the Frechet derivative of the objective functions.