In the present article, we employ the concept of an \(\mathcal {E}\) -LU-optimal solution to explore the nonsmooth semi-infinite interval-valued programming problems. First of all, we formulate the \(\mathcal {E}\) -necessary and \(\mathcal {E}\) -sufficient optimality conditions for the \(\mathcal {E}\) -LU-optimal solution under appropriate convexity and using approximate subdifferentials. After that, we construct the Mond–Weir and Wolfe-type dual models and propose \(\mathcal {E}\) -weak and \(\mathcal {E}\) -strong duality theorems for both the constructed dual models.
