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Research Article | Open Access

Penalty approach for KT-pseudoinvex multidimensional variational control problems

Preeti1, Poonam Agarwal2, Savin Treanţă3,4,5, Kamsing Nonlaopon6( )
Department of Mathematics-SAS, VIT Vellore, Vellore, Tamil Nadu, India
Department of Applied Science and Humanities, Inderprastha Engineering College, Ghaziabad, U.P, India
Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania
"Fundamental Sciences Applied in Engineering" Research Center (SFAI), University Politehnica of Bucharest, 060042 Bucharest, Romania
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
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Abstract

The present paper is the result of a contemplative study of a multi-time control problem (MCP) by considering its associated equivalent auxiliary control problem (MCP) ς via the exact l 1 penalty method. Further study reveals that the solution set of the considered problem and the auxiliary problem exhibits an equivalence under the KT-pseudoinvexity hypothesis. Moreover, the study is extended towards the saddle point defined for (MCP) to establish the relationship between the solution set of multi-time control problem (MCP) and its associated equivalent auxiliary control problem (MCP) ς . Finally, we present an illustrative application to authenticate the results presented in this paper.

Keywords

exact l1 penalty methodKT-pseudoinvexitycontrol problem
CLC number: 26A51, 49J20, 90C30, 90C46

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AIMS Mathematics
Volume 8 Issue 3,
March 2023
Pages 5687-5702
DOI: 10.3934/math.2023286

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Cite this article:
Preeti, Agarwal P, Treanţă S, et al. Penalty approach for KT-pseudoinvex multidimensional variational control problems. AIMS Mathematics, 2023, 8(3): 5687-5702. https://doi.org/10.3934/math.2023286

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Received: 17 August 2022
Revised: 01 December 2022
Accepted: 08 December 2022
Published: 15 March 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)