Journal article
Robust Solutions of Uncertain Quadratic and Conic-Quadratic Problems
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.
Language: | Undetermined |
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Year: | 2002 |
Pages: | 535-560 |
ISSN: | 10957189 and 10526234 |
Types: | Journal article |
DOI: | 10.1137/S1052623401392354 |