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

Nguyen Thi Toan

doi:10.3934/jimo.2021088

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2022, Volume 18, Issue 4: 2705-2720. Doi: 10.3934/jimo.2021088

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

Nguyen Thi Toan^,

School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi, Vietnam

^* Corresponding author: Nguyen Thi Toan
^* Corresponding author: Nguyen Thi Toan

Received: October 31, 2020

Revised: January 31, 2021

Published: July 2022

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Abstract

This paper deals with the generalized Clarke epiderivative of the extremum multifunction of a multi-objective parametric convex discrete optimal control problem with linear state equations and control constraints. By establishing an abstract result on the generalized epiderivative of the extremum multifunction of a multi-objective parametric convex mathematical programming problem, we derive a formula for computing the generalized Clarke epiderivative of the extremum multifunction to a multi-objective parametric convex discrete optimal control problem. Examples are given to illustrate the obtained results.

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Mathematics Subject Classification: Primary: 49K40, 49J53; Secondary: 90C29, 93C55, 93C73.

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