A unified model for robust optimization of linear programs with uncertain parameters

Abstract

This paper presents a general model for unification of the robust counterparts of uncertain linear programs (LP). We extend the robust optimization methodology for LP, introduced by Ben-Tal and Nemirovski, to a unified model in which the uncertainty region is approximated by an appropriate norm body. We derive the robust counterpart of an LP whose parameters may fall in any of the $ l_1,l_2,l_infty $ or matrix-norm bodies. An application to portfolio selection shows how an investor's risk can be measured by a proper norm. Then, various solutions are shown for a practical example. The numerical results indicate that choosing $ l_infty $ norm leads to higher utility for an investor when the uncertainty region is large.