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

Abstract 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