Efficiency criteria and dual techniques for some nonconvex multiple cost minimization models

Abstract

In this study, we investigate a class of multi-objective variational control problems governed by nonconvex simple integral functionals. Concretely, we establish and prove (necessary and sufficient) efficiency criteria and dual techniques for some nonconvex multiple cost minimization models. To this aim, we extend and use the concept of $(\Psi ,\omega )$-invexity to the case of multi-objective variational control problems. Thereafter, by assuming $(\Psi ,\omega )$-invexity, (strictly) $(\Psi ,\omega )$-pseudoinvexity and/or $(\Psi ,\omega )$-quasiinvexity of the involved functionals, we state the sufficient efficiency criteria and associate a dual problem for the considered model.