A Unified Approach Through Image Space Analysis to Robustness in Uncertain Optimization Problems

In this paper, by virtue of the image space analysis, we investigate general scalar robust optimization problems with uncertainties both in the objective and constraints. Under mild assumptions, we characterize various robust solutions for different kinds of robustness concepts, by introducing suitable images of the original uncertain problem, or the images of its counterpart problems appropriately, which provide a unified approach to tackling with robustness for uncertain optimization problems. Several examples are employed to show the effectiveness of the results derived in this paper.