@article{Treanţă2024, 
author = {Savin Treanţă and Cristina-Florentina Marghescu and Laura-Gabriela Matei},
title = {Efficiency conditions in multiple-objective optimal control models under generalized hypotheses},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {9},
pages = {25184-25204},
keywords = {multiple-objective optimal control model, efficiency conditions, generalized hypotheses},
url = {https://www.sciopen.com/article/10.3934/math.20241228},
doi = {10.3934/math.20241228},
abstract = {Since not every problem in optimization theory involves convex functionals, in this study, we introduced new classes of generalized convex functionals. More precisely, under generalized hypotheses, we stated new efficiency conditions associated with a class of multiple-objective optimal control models. To this end, we first defined the  Gθ-Fritz John problem and, by considering it, we established a link between the solutions of  Gθ-Fritz John problem and efficient solutions of the considered model  (P). In addition, we formulated the  Gθ-necessary efficiency conditions for a feasible solution in  (P). After that, we established a connection between the newly defined concept of  Gθ−KT points to  (P) and the efficient solutions of  (P). Finally, we turned our attention to the  Gθ-sufficient efficiency conditions for a feasible solution to  (P). More precisely, we established that any feasible solution to  (P) will be an efficient solution if the assumption of  Gθ-convexity (and/or  Gθ-quasiconvexity,  Gθ-strictly quasiconvexity,  Gθ-monotonic quasiconvexity) is imposed on the involved functionals.}
}