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On Solution Set Associated with a Class of Multiple Objective Control 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, necessary and sufficient efficiency conditions in new multi-cost variational models are formulated and proved. To this end, we introduce a new notion of ( ϑ 0 , ϑ 1 ) − ( σ 0 , σ 1 ) − t y p e − I functionals determined by multiple integrals. To better emphasize the significance of the suggested ( ϑ 0 , ϑ 1 ) − ( σ 0 , σ 1 ) − t y p e − I functionals and how they add to previous studies, we mention that the ( ϑ 0 , ϑ 1 ) − ( σ 0 , σ 1 ) − t y p e − I and generalized ( ϑ 0 , ϑ 1 ) − ( σ 0 , σ 1 ) − t y p e − I − t y p e I assumptions associated with the involved multiple integral functionals cover broader and more general classes of problems, where the convexity of the functionals is not fulfilled or the functionals considered are not of simple integral type. In addition, innovative proofs are provided for the main results.

Suggested Citation

  • Savin Treanţă & Omar Mutab Alsalami, 2025. "On Solution Set Associated with a Class of Multiple Objective Control Models," Mathematics, MDPI, vol. 13(15), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:15:p:2484-:d:1715592
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