Duality and optimality for quasidifferentiable interval-valued problems

In this article, we explore the concept of interval-valued nonsmooth optimization problems using r-invexity in relation to convex compact sets. For the selected nonsmooth interval-valued problem (IP), we derive necessary and sufficient optimality criteria. In addition to that, we establish various duality theorems under r-invex quasidifferentiable with respect to a convex compact set that is equal to the Minkowski sum of their subdifferentials and superdifferentials. We draft a numerical example to support the results obtained in this paper. It is important to note that the Lagrange multipliers are nonconstant for the considered problem.