# Deriving robust and globalized robust solutions of uncertain linear programs with general convex uncertainty sets

We propose a new way to derive tractable robust counterparts of a linear program by using the theory of Beck and Ben-Tal (2009) on the duality between the robust (pessimistic'') primal problem and its optimistic'' dual. First, we obtain a new {\it convex} reformulation of the dual problem of a robust linear program, and then show how to construct the primal robust solution from the dual optimal solution. Our result allows many new uncertainty regions to be considered. We give examples of tractable uncertainty regions that were previously intractable. The results are illustrated by solving a multi-item newsvendor problem. We also apply the new method to the globalized robust counterpart scheme and show its tractability.

## Citation

B. L. Gorissen, A. Ben-Tal, J. P. C. Blanc and D. den Hertog. Deriving robust and globalized robust solutions of uncertain linear programs with general convex uncertainty sets. Operations Research, 62(3), 672-679, 2014.