In this article, we propose a novel technique to analyze saddle point criteria and Wolfe-type duality for a new class of nonsmooth nonconvex problems involving LU- \((\Phi , \rho )\) -invex functions. Namely, the LU- \((\Phi , \rho )\) -approximation method is introduced for nonsmooth multiobjective interval-valued mathematical problems to characterize their (weakly) LU-efficient solutions. In this approach, we construct an LU- \((\Phi , \rho )\) -approximated nonsmooth problem at a given feasible solution of the original problem. We establish an equivalence between the saddle point of the approximated problem and the LU-efficient solution of the original considered problem by introducing the concept of the LU-Lagrange function. Additionally, we formulate Wolfe-type dual problem corresponding to both the original and approximated problems. Furthermore, the introduced LU- \((\Phi , \rho )\) -approximation method is utilized to derive several duality results in the sense Wolfe-type duality. Finally, an application is provided to illustrate the established results numerically.
