On constraint qualifications and optimality conditions for robust optimization problems through pseudo-differential

In this paper, a nonsmooth nonconvex robust optimization problem is considered. Using the idea of pseudo-differential, nonsmooth versions of the Robinson, Mangasarian-Fromovitz and Abadie constraint qualifications are introduced and their relations with the existence of a local error bound are investigated. Based on the pseudo-differential notion, new necessary optimality conditions are derived under the Abadie constraint qualification. Moreover, an example is provided to clarify the results.