Our objective in the present article is to reframe the ideology of the \({\mathcal {E}}\) -LU-Pareto solution for nonsmooth semi-infinite programs with multiple intervals. First of all, using the scalarization method, we establish the relation between the \({\mathcal {E}}\) -LU-Pareto solution and the \({\mathcal {E}}\) -LU-optimal solution. Moreover, we figure out \({\mathcal {E}}\) -necessary and sufficient optimality conditions under the constraint qualification named Farkas-Minkowski using the notion of approximate subdifferentials. Additionally, we construct a dual model with the mixed-type approximation that combines features of both the Mond-Weir and Wolfe-type dual formulations. Subsequently, we derive weak and strong duality results within the context of convexity and generalized convexity. Finally, we show that the projected mixed dual model can be transformed into both the Mond-Weir and Wolfe-type dual models.
