  We consider solving linear optimization (LO) problems with uncertain
objective coefficients. For such problems, we often employ robust optimization
(RO) approaches by introducing an uncertainty set for the unknown coefficients.
Typical RO approaches require observations or prior knowledge of the unknown
coefficient to define an appropriate uncertainty set. However, such information
may not always be available in practice. In this study, we propose a novel
uncertainty set for robust linear optimization (RLO) problems without prior
knowledge of the unknown coefficients. Instead, we assume to have data of known
constraint parameters and corresponding optimal solutions. Specifically, we
derive an explicit form of the uncertainty set as a polytope by applying
techniques of inverse optimization (IO). We prove that the RLO problem with the
proposed uncertainty set can be equivalently reformulated as an LO problem.
Numerical experiments show that the RO approach with the proposed uncertainty
set outperforms classical IO in terms of performance stability.

Optimization and Control