Robust Solutions of Uncertain Quadratic and Conic-Quadratic Problems

Authors:
A. Ben-Tal;A. Nemirovski;C. Roos
Affiliations:
-;-;-
Venue:
SIAM Journal on Optimization
Year:
2002

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Abstract

We consider a conic-quadratic (and in particular a quadratically constrained) optimization problem with uncertain data, known only to reside in some uncertainty set ${\cal U}$. The robust counterpart of such a problem leads usually to an NP-hard semidefinite problem; this is the case, for example, when ${\cal U}$ is given as the intersection of ellipsoids or as an n-dimensional box. For these cases we build a single, explicit semidefinite program, which approximates the NP-hard robust counterpart, and we derive an estimate on the quality of the approximation, which is essentially independent of the dimensions of the underlying conic-quadratic problem.