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Results on Solution Set in Certain Interval-Valued Controlled Models

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  • Savin Treanţă

    (Department Applied Mathematics, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania
    Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania
    Fundamental Sciences Applied in Engineering Research Center, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania)

  • Omar Mutab Alsalami

    (Department of Electrical Engineering, College of Engineering, Taif University, Taif 21944, Saudi Arabia)

Abstract

In this paper, a class of controlled variational control models is studied by considering the notion of ( q , w ) − π -invexity. Our aim is to investigate a solution set in the considered interval-valued controlled models. To achieve this, we establish some characterization results of solutions in the controlled interval-valued variational models. More precisely, necessary and sufficient conditions of optimality are highlighted as part of a feasible solution. To prove that the optimality conditions are sufficient, we impose generalized invariant convexity hypotheses for the involved multiple integral functionals. Finally, a duality result is provided in order to better describe the problem under study. The methodology used in this paper is a combination of techniques from the Lagrange–Hamilton theory, calculus of variations, and control theory. This study could be immediately improved by including an analysis of this class of optimization problems by using curvilinear integrals instead of multiple integrals. The independence of path imposed to these functionals and their physical significance would increase the applicability and importance of the paper.

Suggested Citation

  • Savin Treanţă & Omar Mutab Alsalami, 2025. "Results on Solution Set in Certain Interval-Valued Controlled Models," Mathematics, MDPI, vol. 13(2), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:202-:d:1563621
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    References listed on IDEAS

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    1. A. Charnes & Frieda Granot & F. Phillips, 1977. "An Algorithm for Solving Interval Linear Programming Problems," Operations Research, INFORMS, vol. 25(4), pages 688-695, August.
    2. Savin Treanţă, 2022. "Characterization results of solutions in interval-valued optimization problems with mixed constraints," Journal of Global Optimization, Springer, vol. 82(4), pages 951-964, April.
    3. Savin Treanţă & Tareq Saeed, 2023. "On Weak Variational Control Inequalities via Interval Analysis," Mathematics, MDPI, vol. 11(9), pages 1-11, May.
    4. Chanas, Stefan & Kuchta, Dorota, 1996. "Multiobjective programming in optimization of interval objective functions -- A generalized approach," European Journal of Operational Research, Elsevier, vol. 94(3), pages 594-598, November.
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