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Robust Convex Optimization
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.
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Citations
Cited by
Robust optimization ? methodology and applications
Ben-Tal, A., & Nemirovski, A. (2002) · Mathematical Programming · doi:10.1007/s101070100286 · Cited by 1,409
Self-citationAdjustable robust solutions of uncertain linear programs
Ben-Tal, A., Goryashko, A., Guslitzer, E., & Nemirovski, A. (2004) · Mathematical Programming · doi:10.1007/s10107-003-0454-y · Cited by 1,380
Self-citationRobust minimum variance beamforming
Lorenz, R. G., & Boyd, S. P. (2005) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2005.845436 · Cited by 774
Distributionally Robust Optimization and Its Tractable Approximations
Goh, J., & Sim, M. (2010) · Operations Research · doi:10.1287/opre.1090.0795 · Cited by 668
Uncertain convex programs: randomized solutions and confidence levels
Calafiore, G., & Campi, M. C. (2005) · Mathematical Programming · doi:10.1007/s10107-003-0499-y · Cited by 659
Metadata
- Authors
- Ben-Tal, A., & Nemirovski, A.
- Venue
- Mathematics of Operations Research
- Published
- 1998-11
- Volume
- 23
- Issue
- 4
- Pages
- 769-805
- ISSN
- 0364-765X (ISSN-L)
- 1526-5471
- OpenAlex
- W2089105401
- Cited by
- 2,598
- References
- 0
- FWCI
- 8.96
- Type
- journal article
- Language
- en
- Open access
- closed
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- Ben-Tal, A., & Nemirovski, A. (1998). Robust Convex Optimization. Mathematics of Operations Research. https://doi.org/10.1287/moor.23.4.769
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