We deal with some advanced tools of variational analysis and new generalized differentiation to formulate robust necessary and sufficient \(\epsilon -\) optimality conditions for robust \(\epsilon -\) quasi Pareto solutions of a nonsmooth semi-infinite multiobjective optimization problem under data uncertainty ((UGMP) for shortly), where \(\epsilon \) is a non-negative real number. For this purpose, a new version of the robust regularity condition (RC) is introduced and a sufficient condition for the (RC) is provided. Besides, we establish the robust necessary \(\epsilon -\) optimality conditions for (UGMP) through the Aubin-Frankowska subdifferentials in which the involved functions are steady. Under suitable assumptions on the \(\epsilon -\) pseudoconvexity in which the involved functions are stable, the robust necessary \(\epsilon -\) optimality conditions become the robust sufficient \(\epsilon -\) optimality conditions. Additionally, a Mond-Weir-type dual robust multiobjective problem for the primal problem is constructed and robust \(\epsilon -\) quasi weak, strong, and converse duality relations among them are explored. Some illustrative examples are proposed for our findings.
