El Ghaoui, Laurent; Lebret, Hervé Robust solutions to least-squares problems with uncertain data. (English) Zbl 0891.65039 SIAM J. Matrix Anal. Appl. 18, No. 4, 1035-1064 (1997). Least-squares problems are studied where the coefficient matrices are unknown but bounded. The worse-case residual error is minimized. The exact value of the optimal worst-case residuals is computed using convex, second-order cone programming or semidefinite programming. A consequence is that the minimizing vector can be computed in polynomial time. Reviewer: H.Hollatz (Magdeburg) Cited in 1 ReviewCited in 218 Documents MSC: 65F20 Numerical solutions to overdetermined systems, pseudoinverses 65Y20 Complexity and performance of numerical algorithms Keywords:least-squares problems; uncertainty; robustness; semidefinite programming; ill-conditioned problem; regularization; robust interpolation PDF BibTeX XML Cite \textit{L. El Ghaoui} and \textit{H. Lebret}, SIAM J. Matrix Anal. Appl. 18, No. 4, 1035--1064 (1997; Zbl 0891.65039) Full Text: DOI OpenURL