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Reciprocal Theorems for Multi-Cost Problems with S -Type I Functionals

Author

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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)

  • Valeria Cîrlan

    (Department Applied Mathematics, 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, for the considered multi-cost variational problem (P), we associate a dual model (D) in order to study and state the connections between the solution sets of these control problems. Thus, under S -type I assumptions associated with the integral functionals involved, we formulate and prove various reciprocal results, such as weak, strong, and converse-type dualities.

Suggested Citation

  • Savin Treanţă & Valeria Cîrlan & Omar Mutab Alsalami, 2025. "Reciprocal Theorems for Multi-Cost Problems with S -Type I Functionals," Mathematics, MDPI, vol. 13(14), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:14:p:2250-:d:1699766
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    References listed on IDEAS

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    1. Ali Sadeghieh & Nader Kanzi & Giuseppe Caristi & David Barilla, 2022. "On stationarity for nonsmooth multiobjective problems with vanishing constraints," Journal of Global Optimization, Springer, vol. 82(4), pages 929-949, April.
    2. Le Thanh Tung, 2022. "Karush–Kuhn–Tucker optimality conditions and duality for multiobjective semi-infinite programming with vanishing constraints," Annals of Operations Research, Springer, vol. 311(2), pages 1307-1334, April.
    3. S. K. Mishra & Vinay Singh & Vivek Laha, 2016. "On duality for mathematical programs with vanishing constraints," Annals of Operations Research, Springer, vol. 243(1), pages 249-272, August.
    4. Khadija Khazafi & Norma Rueda & Per Enflo, 2010. "Sufficiency and duality for multiobjective control problems under generalized (B, ρ)-type I functions," Journal of Global Optimization, Springer, vol. 46(1), pages 111-132, January.
    5. Tamanna Yadav & S. K. Gupta & Sumit Kumar, 2024. "Optimality analysis and duality conditions for a class of conic semi-infinite program having vanishing constraints," Annals of Operations Research, Springer, vol. 340(2), pages 1091-1123, September.
    6. K. Khazafi & N. Rueda, 2009. "Multiobjective Variational Programming under Generalized Type I Univexity," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 363-376, August.
    7. Tadeusz Antczak, 2015. "Sufficient optimality criteria and duality for multiobjective variational control problems with $$G$$ G -type I objective and constraint functions," Journal of Global Optimization, Springer, vol. 61(4), pages 695-720, April.
    8. Najeeb Abdulaleem & Savin Treanţă, 2023. "Optimality conditions and duality for E-differentiable multiobjective programming involving V-E-type I functions," OPSEARCH, Springer;Operational Research Society of India, vol. 60(4), pages 1824-1843, December.
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