Penalty approach for KT-pseudoinvex multidimensional variational control problems

Preeti; Poonam Agarwal; Savin Treanţă; Kamsing Nonlaopon; Preeti; Poonam Agarwal; Savin Treanţă; Kamsing Nonlaopon

doi:10.3934/math.2023286

AIMS Mathematics

2023, Volume 8, Issue 3: 5687-5702. doi: 10.3934/math.2023286

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Research article

Penalty approach for KT-pseudoinvex multidimensional variational control problems

1.
Department of Mathematics-SAS, VIT Vellore, Vellore, Tamil Nadu, India
2.
Department of Applied Science and Humanities, Inderprastha Engineering College, Ghaziabad, U.P, India
3.
Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
4.
Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania
5.
"Fundamental Sciences Applied in Engineering" Research Center (SFAI), University Politehnica of Bucharest, 060042 Bucharest, Romania
6.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 17 August 2022 Revised: 01 December 2022 Accepted: 08 December 2022 Published: 22 December 2022
MSC : 26A51, 49J20, 90C30, 90C46

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)$ _{\varsigma} $ 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)$ _{\varsigma} $. Finally, we present an illustrative application to authenticate the results presented in this paper.
- exact $ l_{1} $ penalty method,
- KT-pseudoinvexity,
- control problem
Citation: Preeti, Poonam Agarwal, Savin Treanţă, Kamsing Nonlaopon. Penalty approach for KT-pseudoinvex multidimensional variational control problems[J]. AIMS Mathematics, 2023, 8(3): 5687-5702. doi: 10.3934/math.2023286

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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)$ _{\varsigma} $ 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)$ _{\varsigma} $. Finally, we present an illustrative application to authenticate the results presented in this paper.

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