
Mathematics 2015
Stability and Continuity in Robust Linear and Linear SemiInfinite OptimizationAbstract: We consider the stability of Robust Optimization problems with respect to perturbations in their uncertainty sets. We focus on Linear Optimization problems, including those with a possibly infinite number of constraints, also known as Linear SemiInfinite Optimization (LSIO) problems, and consider uncertainty in both the cost function and constraints. We prove Lipschitz continuity of the optimal value and {\epsilon}approximate optimal solution set with respect to the Hausdorff distance between uncertainty sets and with an explicit Lipschitz constant that can be calculated. In addition, we prove closedness and upper semicontinuity for the optimal solution set mapping with respect to the uncertainty set.
