Dual Approaches to Characterize Robust Optimal Solution Sets for a Class of Uncertain Optimization Problems

Abstract

In this paper, we deal with robust optimal solution sets for a class of optimization problems with data uncertainty in both the objective and constraints. We first introduce a mixed-type robust dual problem of this class of uncertain optimization problems and explore robust strong duality relations between them. Then, we propose a new approach to characterize robust optimal solution sets of this class of uncertain optimization problems via its dual problem. Moreover, we show that several results on characterizations of robust optimal solution sets of uncertain optimization problems obtained in recent literature can be obtained using our approach.