In this study, we focus on the approximation approach for non-convex \(E\) -differentiable variational problems. In this method, we construct a new \(E\) -differentiable variational problem by modifying the objective function of the initial problem. We establish an equivalence between the \(E\) -optimal solution to the initial variational problem and its related \(E\) -modified variational problem using the assumption of \(E\) -invexity. Thereafter, we investigate the \(E\) -modified saddle point results using the concept of Lagrange function. The utility of this transformation lies in the fact that it converts objective function of variational problems to modified objective function ones. To accurately predict the applicability of the results presented in the paper, meticulously crafted examples are provided.
