Sufficient Efficiency Criteria for New Classes of Non-Convex Optimization Models

In this paper, we introduce and study a new class of minimization models driven by multiple integrals as cost functionals. Concretely, we formulate and establish some sufficient efficiency criteria for a feasible point in the considered optimization problem. To this end, we introduce and define the concepts of (Γ,ψ)-invexity and generalized (Γ,ψ)-invexity for the involved real-valued controlled multiple integral-type functionals. More precisely, we extend the notion of (generalized) (Γ,ψ)-invexity to the multiple objective control models driven by multiple integral functionals. In addition, innovative proofs are considered for the principal results derived in the paper.