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Robust convex optimization (1998)
| Venue: | Mathematics of Operations Research |
| Citations: | 416 - 21 self |
BibTeX
@ARTICLE{Ben-tal98robustconvex,
author = {A. Ben-tal and A. Nemirovski},
title = {Robust convex optimization},
journal = {Mathematics of Operations Research},
year = {1998},
volume = {23},
pages = {769--805}
}
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Abstract
We study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set U, yet the constraints must hold for all possible values of the data from U. The ensuing optimization problem is called robust optimization. In this paper we lay the foundation of robust convex optimization. In the main part of the paper we show that if U is an ellipsoidal uncertainty set, then for some of the most important generic convex optimization problems (linear programming, quadratically constrained programming, semidefinite programming and others) the corresponding robust convex program is either exactly, or approximately, a tractable problem which lends itself to efficient algorithms such as polynomial time interior point methods.
Keyphrases
robust convex optimization semidefinite programming tractable problem possible value polynomial time interior point method linear programming optimization problem robust optimization corresponding robust convex program main part important generic convex optimization problem convex optimization problem ellipsoidal uncertainty
