Reciprocal results for the study of some optimization models

Abstract This paper studies various reciprocal results for the study of some optimization models, recently introduced and partial investigated in (Treanţă and Alsalami, Math (2025)). We state some duality relationships between the considered dual models and the primal/original family of optimization problems. The presence of control variables and the innovative proofs associated with the principal results derived in this study give the essential and crucial role of this research paper, compared with the previous research works.