Efficiency conditions in new interval-valued control models via modified T-objective functional approach and saddle-point criteria

The paper studied efficiency conditions in new interval-valued control models via a modified T-objective functional approach and saddle-point type criteria. More precisely, first, by considering the necessary optimality conditions associated to single-objective variational control models with interval values, we formulated the necessary efficiency conditions for a new control model, denoted by $ (P) $, with multiple cost interval-valued functionals. Thereafter, by considering the notions of T-convexity and T-pseudoconvexity, with T as a sublinear functional (with respect to the sixth and seventh variable), we formulated a characterization result of saddle-point for a Lagrange functional associated with $ (P) $. Further, we established sufficient efficiency conditions for $ (P) $ via the modified T-objective functional approach. Finally, under suitable generalized convexity assumptions, we stated the connection between a Lower-Upper-efficient solution (in short, $ LU $-efficient solution) for $ (P) $ and a saddle-point for the Lagrange functional associated with the modified control model.