Characterizations of Approximate Optimality Conditions for Fractional Semi-Infinite Optimization Problems With Uncertainty

Abstract

This paper is devoted to the investigation of a class of multi-objective fractional semi-infinite optimization problems with uncertain data. Firstly, a robust counterpart for the uncertain multi-objective optimization problem is introduced in terms of robust optimization method. And following the idea due to Dinkelbach, we associate the robust counterpart with a multi-objective optimization problem. Then, by using a scalarization method, its corresponding scalarization optimization problem is established. The relationship between robust solutions of the multi-objective optimization problem and that of its corresponding scalarization optimization problem is described. Finally, by using a robust type sub-differential constraint qualification, the robust optimality condition for approximate quasi-efficient solutions of the multi-objective fractional optimization problem is established.