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

Nguyen Thi Toan () and Le Quang Thuy ()
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Nguyen Thi Toan: Hanoi University of Science and Technology
Le Quang Thuy: Hanoi University of Science and Technology

Journal of Optimization Theory and Applications, 2023, vol. 196, issue 1, No 11, 240-265

Abstract: Abstract 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 Fréchet 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.

Keywords: Multi-objective parametric discrete optimal control problem; Extremum multifunction; Efficient point multifunction; S-derivative; Sensitivity analysis; 49K40; 49J53; 90C29; 93C55; 93C73 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-022-02130-y

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