This paper is devoted to propose and investigate an \(l_{1}\) exact penalty method for a class of E-differentiable constrained interval-valued programming problems with both inequality and equality constraints. The aforesaid programming problems are transformed into an unconstrained interval-valued penalized optimization problem using the E-function approach. However, its constituent functions are E-differentiable, but they are not necessarily differentiable. Then, we examine the most significant property of all penalization interval-valued exactness. From a practical point of view, this is very important for all exact penalty function techniques, that is, exactness of the penalization. Under some relevant conditions, we establish the equivalence between an E-optimal solution of interval-valued primal and its corresponding penalized E-optimization problem. The utility of this transformation lies in the fact that it converts constrained problems to unconstrained ones. To accurately predict the applicability of the results presented in the paper, meticulously crafted examples are provided.
