Abstract
Using a scheme for solving multiobjective optimization problems via a system of corresponding scalar problems, approximate optimality conditions for a nonconvex semi-infinite multiobjective optimization problem are established. As a new approach, the scheme is developed to study the approximate duality theorems of the problem via a pair of primal-dual scalar problems. Several $\epsilon$-duality theorems are given. Furthermore, the existence theorem for almost quasi weakly $\epsilon$-Pareto solutions of the primal problem, and the existence theorem for quasi weakly $\epsilon$-Pareto solutions of the dual problem are established without any constraint qualification.
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