Connections between Some Extremization Problems and Associated Inequalities

Abstract

In this paper, we investigate and characterize a family of optimization problems introduced by interval-valued functionals that are determined by curvilinear integrals. To this end, we first state the path independence and (strictly) LU convexity properties of the considered functionals. Thereafter, we formulate the corresponding controlled variational inequalities. The main results of this paper provide some connections for the above-mentioned variational models. Since the objective functionals have a physical importance, an illustrative application is considered and studied by using the theoretical elements obtained in this study.

Keywords

• path independence
• <i>LU</i> convexity
• variational inequality
• optimal solution