Characterizing robust set containments and solutions of uncertain linear programs without qualifications

Abstract

Qualification-free dual characterizations are given for robust polyhedral set containments where a robust counterpart of an uncertain polyhedral set is contained in another polyhedral set or a polyhedral set is contained in a robust counterpart of an uncertain polyhedral set. These results are used to characterize robust solutions of uncertain linear programs, where the uncertainty is defined in terms of intervals or l 1 -balls. The hidden separable sub-linearity of the robust counterparts allows qualification-free dual characterizations.