The DOI matches its Crossref record; 18 of the 18 references it cites were found in a registry or an index.
Robust Solutions to Least-Squares Problems with Uncertain Data
Abstract
We consider least-squares problems where the coefficient matrices A,b are unknown but bounded. We minimize the worst-case residual error using (convex) second-order cone programming, yielding an algorithm with complexity similar to one singular value decomposition of A. The method can be interpreted as a Tikhonov regularization procedure, with the advantage that it provides an exact bound on the robustness of solution and a rigorous way to compute the regularization parameter. When the perturbation has a known (e.g., Toeplitz) structure, the same problem can be solved in polynomial-time using semidefinite programming (SDP). We also consider the case when A,b are rational functions of an unknown-but-bounded perturbation vector. We show how to minimize (via SDP) upper bounds on the optimal worst-case residual. We provide numerical examples, including one from robust identification and one from robust interpolation.
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Cites
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Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611970777 · Cited by 21,687
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Robust Solutions to Uncertain Semidefinite Programs
El Ghaoui, L., Oustry, F., & Lebret, H. (1998) · SIAM Journal on Optimization · doi:10.1137/s1052623496305717 · Cited by 935
Self-citationRobustness in the presence of mixed parametric uncertainty and unmodeled dynamics
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Cited by
Bertsimas, D., & Sim, M. (2004) · Operations Research · doi:10.1287/opre.1030.0065 · Cited by 4,557
Robust solutions of Linear Programming problems contaminated with uncertain data
Ben-Tal, A., & Nemirovski, A. (2000) · Mathematical Programming · doi:10.1007/pl00011380 · Cited by 1,744
Adjustable 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
Robust Solutions to Uncertain Semidefinite Programs
El Ghaoui, L., Oustry, F., & Lebret, H. (1998) · SIAM Journal on Optimization · doi:10.1137/s1052623496305717 · Cited by 935
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
Metadata
- Authors
- El Ghaoui, L., & Lebret, H.
- Venue
- SIAM Journal on Matrix Analysis and Applications
- Published
- 1997-10
- Volume
- 18
- Issue
- 4
- Pages
- 1035-1064
- ISSN
- 0895-4798 (ISSN-L)
- 1095-7162
- OpenAlex
- W2048679451
- Cited by
- 1,076
- References
- 18
- FWCI
- 11.36
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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