In this paper we apply some tools of nonsmooth analysis and scalarization method due to Chankong-Haimes \cite{Ch} to find $\epsilon$-efficient solutions of semi-infinite multiobjective optimization problems (MP). We establish $\epsilon$-optimality conditions of Kuhn-Karush-Tucker (KKT) type under FM constraint qualification by using $\epsilon$-subdifferential concept. In addition we propose types of Wolfe, Mond-Weir and Mixed dual problems for $\epsilon$-efficient solutions and investigate relationship between mentioned (MP) and its dual problems as well as establish $\epsilon$-duality theorem.