Robust optimization: sensitivity to uncertainty in scalar and vector cases, with applications

The question we address is how robust solutions react to changes in the uncertainty set. We prove the location of robust solutions with respect to the magnitude of a possible decrease in uncertainty, namely when the uncertainty set shrinks, and convergence of the sequence of robust solutions. In decision making, uncertainty may arise from incomplete information about people's (stakeholders, voters, opinion leaders, etc.) perception about a specific issue. Whether the decision maker (DM) has to look for the approval of a board or pass an act, they might need to define the strategy that displeases the minority. In such a problem, the feasible region is likely to unchanged, while uncertainty affects the objective function. Hence the paper studies only this framework.