On Generalised Minty Variational Control Inequalities and the Associated Multi-Cost Models

Abstract

In this study, by using the concepts of (strictly) strongly convexity and preconvexity, associated with controlled multiple integral type functionals, and a mean value type theorem, we formulate some connections between new classes of generalised Minty (weak) variational inequalities of vector-type and the corresponding multiple-objective extremization problems. The considered classes of variational models are motivated by their applications in real-world modelling problems. The presence of control variables and controlled multiple integrals are the main tools in establishing the new outcomes.