Abstract: We considered a class of semi-infinite multi-objective optimization problems with uncertain data. We first introduced a robust approximate Pareto weak efficient solution of the uncertain semi-infinite multi-objective optimization problem. Then, by means of a robust-type subdifferential constraint qualification and a class of generalized convexity assumptions, we gave necessary and sufficient optimality conditions for the robust approximate quasi Pareto weak efficient solution of the multi-objective optimization problem.

Key words: semi-infinite optimization problem, quasi Pareto weak efficient solution, generalized convexity