## Robust Solutions To Least-Squares Problems With Uncertain Data (1997)

Citations: | 148 - 12 self |

### BibTeX

@MISC{Ghaoui97robustsolutions,

author = {Laurent El Ghaoui and Hervé Lebret},

title = {Robust Solutions To Least-Squares Problems With Uncertain Data},

year = {1997}

}

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### OpenURL

### Abstract

. We consider least-squares problems where the coefficient matrices A; b are unknown-butbounded. 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. Key Words. Least-squares, uncertainty, robustness, second-order cone...