The Clarke Coderivative of the Frontier Map in a Multi-objective Optimal Control Problem

Motivated by our recent works on the efficient point multifunction in multi-objective parametric optimal control problems with nonconvex cost functions and control constrains, in this paper we study of the first-order behavior of the efficient point multifunction in a multi-objective parametric opti...

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Bibliographic Details
Published in:Applied mathematics & optimization Vol. 88; no. 2; p. 42
Main Authors: Toan, N. T., Thuy, L. Q.
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2023
Springer Nature B.V
Subjects:
Applied mathematics
Calculus of Variations and Optimal Control; Optimization
Control
Cost function
Energy consumption
Equations of state
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical programming
Mathematics
Mathematics and Statistics
Multiple objective analysis
Nonlinear control
Numerical and Computational Physics
Optimal control
Optimization
Sensitivity analysis
Simulation
Systems Theory
Theoretical
90C31
Multi-objective parametric optimal control problem
49J53
93C15
The Frontier map
Clarke coderivative
Clarke normal cone
Clarke tangent cone
34K35
90B50
Efficient point multifunction
ISSN:0095-4616, 1432-0606
Online Access:Get full text
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Summary:Motivated by our recent works on the efficient point multifunction in multi-objective parametric optimal control problems with nonconvex cost functions and control constrains, in this paper we study of the first-order behavior of the efficient point multifunction in a multi-objective parametric optimal control problem under nonlinear state equations. By establishing an abstract result on the Clarke coderivative of the frontier map of a multi-objective parametric mathematical programming problem, we derive a formula for computing the Clarke coderivative of the efficient point multifunction to a multi-objective parametric optimal control problem.
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ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-023-10020-6