Robust second order duality for a non-differentiable fractional programming with complex variables

In this piece of work, we consider a non-differentiable fractional programming problem under uncertainty of data in a complex space. On the framework of the worst-case scenario, we use the robust optimization approach to construct its robust counterpart problem. Given the significance of a duality-based model of a programming problem, we introduce the "robust-Karush-Kuhn-Tucker" necessary optimality conditions and employ them to create a robust second-order, briefly 2nd-order, Mangasarian-type dual model of the considered problem. Eventually, the theorems of robust strong, weak, and strict converse duality are formulated and demonstrated. Finally, we suggest a potential direction for future study in complex spaces with problems involving multi-objective fractional programming when uncertain data is present.