On Solution Set Associated with a Class of Multiple Objective Control Models

Savin Treanţă () and Omar Mutab Alsalami ()
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Savin Treanţă: 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

Mathematics, 2025, vol. 13, issue 15, 1-13

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.

Keywords: efficiency conditions; multi-cost variational models; multiple integrals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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