New classes of interval-valued variational problems and inequalities

Abstract

The paper discusses two distinct classes of variational problems. The first class focuses on optimization problems governed by interval-valued functionals, which are influenced by second-order partial derivatives. The second class pertains to variational inequalities associated with the first class. The paper explores relationships between solutions within these variational models and introduces the concept of convexity assumption for interval-valued functionals. The significance of these findings lies in the practical applications, particularly in the context of objective functionals with physical implications, such as the computation of mechanical work.

Keywords

• Optimization problem
• Path-independence
• Variational inequality
• LU-convexity
• LU-optimal solution