Robust linear optimization under general norms

Authors:
Dimitris Bertsimas;Dessislava Pachamanova;Melvyn Sim
Affiliations:
Sloan School of Management, Massachusetts Institute of Technology, Building E52-363, 50 Memorial Drive, Cambridge, MA 02142-1347, USA;Department of Mathematics and Sciences, Babson College, Forest Street, Babson Park, MA 02457, USA;NUS Business School, National University of Singapore, 1 Business Link, Singapore 117592, Singapore
Venue:
Operations Research Letters
Year:
2004

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Abstract

We explicitly characterize the robust counterpart of a linear programming problem with uncertainty set described by an arbitrary norm. Our approach encompasses several approaches from the literature and provides guarantees for constraint violation under probabilistic models that allow arbitrary dependencies in the distribution of the uncertain coefficients.