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This paper provides some new results on robust approximate optimal solutions of a fractional semi-infinite optimization problem under uncertainty data in the constraint functions. By employing conjugate analysis and robust optimization approach (worst-case approach), we obtain some necessary and sufficient optimality conditions for robust approximate optimal solutions of such a fractional semi-infinite optimization problem. In addition, we state a mixed type approximate dual problem to the reference problem and obtain some robust duality properties between them. The results obtained in this paper improve the corresponding results in the literature.

On robust approximate optimal solutions for fractional semi-infinite optimization with uncertainty data