Efficiency conditions in new interval-valued control models via modified $ T $-objective functional approach and saddle-point criteria

Savin Treanţă; Cristina-Florentina Pîrje; Jen-Chih Yao; Balendu Bhooshan Upadhyay; Savin Treanţă; Cristina-Florentina Pîrje; Jen-Chih Yao; Balendu Bhooshan Upadhyay

doi:10.3934/mmc.2025013

Mathematical Modelling and Control

2025, Volume 5, Issue 2: 180-192. doi: 10.3934/mmc.2025013

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Research article

Efficiency conditions in new interval-valued control models via modified $ T $-objective functional approach and saddle-point criteria

1.
Department of Applied Mathematics, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania
2.
Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania
3.
Fundamental Sciences Applied in Engineering - Research Center, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania
4.
Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichuug, Taiwan
5.
Department of Mathematics, Indian Institute of Technology Patna, Patna, India

Received: 02 April 2024 Revised: 30 August 2024 Accepted: 09 October 2024 Published: 26 May 2025

The paper studied efficiency conditions in new interval-valued control models via a modified $ T $-objective functional approach and saddle-point type criteria. More precisely, first, by considering the necessary optimality conditions associated to single-objective variational control models with interval values, we formulated the necessary efficiency conditions for a new control model, denoted by $ (P) $, with multiple cost interval-valued functionals. Thereafter, by considering the notions of $ T $-convexity and $ T $-pseudoconvexity, with $ T $ as a sublinear functional (with respect to the sixth and seventh variable), we formulated a characterization result of saddle-point for a Lagrange functional associated with $ (P) $. Further, we established sufficient efficiency conditions for $ (P) $ via the modified $ T $-objective functional approach. Finally, under suitable generalized convexity assumptions, we stated the connection between a Lower-Upper-efficient solution (in short, $ LU $-efficient solution) for $ (P) $ and a saddle-point for the Lagrange functional associated with the modified control model.
- control,
- saddle-point,
- interval-valued functional
Citation: Savin Treanţă, Cristina-Florentina Pîrje, Jen-Chih Yao, Balendu Bhooshan Upadhyay. Efficiency conditions in new interval-valued control models via modified $ T $-objective functional approach and saddle-point criteria[J]. Mathematical Modelling and Control, 2025, 5(2): 180-192. doi: 10.3934/mmc.2025013

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Abstract

The paper studied efficiency conditions in new interval-valued control models via a modified $ T $-objective functional approach and saddle-point type criteria. More precisely, first, by considering the necessary optimality conditions associated to single-objective variational control models with interval values, we formulated the necessary efficiency conditions for a new control model, denoted by $ (P) $, with multiple cost interval-valued functionals. Thereafter, by considering the notions of $ T $-convexity and $ T $-pseudoconvexity, with $ T $ as a sublinear functional (with respect to the sixth and seventh variable), we formulated a characterization result of saddle-point for a Lagrange functional associated with $ (P) $. Further, we established sufficient efficiency conditions for $ (P) $ via the modified $ T $-objective functional approach. Finally, under suitable generalized convexity assumptions, we stated the connection between a Lower-Upper-efficient solution (in short, $ LU $-efficient solution) for $ (P) $ and a saddle-point for the Lagrange functional associated with the modified control model.

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