Polyhedral approximation of ellipsoidal uncertainty sets via extended formulations: a computational case study

Andreas Bärmann (), Andreas Heidt (), Alexander Martin (), Sebastian Pokutta () and Christoph Thurner ()
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Andreas Bärmann: FAU Erlangen-Nürnberg
Andreas Heidt: FAU Erlangen-Nürnberg
Alexander Martin: FAU Erlangen-Nürnberg
Sebastian Pokutta: Georgia Institute of Technology
Christoph Thurner: FAU Erlangen-Nürnberg

Computational Management Science, 2016, vol. 13, issue 2, No 2, 193 pages

Abstract: Abstract Robust optimization is an important technique to immunize optimization problems against data uncertainty. In the case of a linear program and an ellipsoidal uncertainty set, the robust counterpart turns into a second-order cone program. In this work, we investigate the efficiency of linearizing the second-order cone constraints of the latter. This is done using the optimal linear outer-approximation approach by Ben-Tal and Nemirovski (Math Oper Res 26:193–205, 2001) from which we derive an optimal inner approximation of the second-order cone. We examine the performance of this approach on various benchmark sets including portfolio optimization instances as well as (robustified versions of) the MIPLIB and the SNDlib.

Keywords: Robust optimization; Approximation; Extended formulations; Second-order cone optimization; Mixed-integer programming; Portfolio optimization; 90C31; 90C59; 90C20; 90C11 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10287-015-0243-0

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