, Volume 97, Issue 3, pp 495-515
Date: 07 May 2003

Robust convex quadratically constrained programs

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Abstract.

In this paper we study robust convex quadratically constrained programs, a subset of the class of robust convex programs introduced by Ben-Tal and Nemirovski [4]. In contrast to [4], where it is shown that such robust problems can be formulated as semidefinite programs, our focus in this paper is to identify uncertainty sets that allow this class of problems to be formulated as second-order cone programs (SOCP). We propose three classes of uncertainty sets for which the robust problem can be reformulated as an explicit SOCP and present examples where these classes of uncertainty sets are natural.

Research partially supported by DOE grant GE-FG01-92ER-25126, NSF grants DMS-94-14438, CDA-97-26385, DMS-01-04282 and ONR grant N000140310514.
Research partially supported by NSF grants CCR-00-09972, DMS-01-04282 and ONR grant N000140310514.