On $${\epsilon}$$ -solutions for convex optimization problems with uncertainty data

Abstract

We consider \({\epsilon}\) -solutions (approximate solutions) for a robust convex optimization problem in the face of data uncertainty. Using robust optimization approach (worst-case approach), we establish an optimality theorem and duality theorems for \({\epsilon}\) -solutions for the robust convex optimization problem. Moreover, we give an example illustrating the duality theorems.