de Klerk, Etienne; Laurent, Monique A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis. (English) Zbl 1436.90099 Araujo, Carolina (ed.) et al., World women in mathematics 2018. Proceedings of the first world meeting for women in mathematics (WM)\({}^2\), a satellite conference of ICM, Rio de Janeiro, Brazil, July 31, 2018. Dedicated to the memory of Maryam Mirzakhani. Cham: Springer. Assoc. Women Math. Ser. 20, 17-56 (2019). MSC: 90C22 65K05 90-02 PDFBibTeX XMLCite \textit{E. de Klerk} and \textit{M. Laurent}, Assoc. Women Math. Ser. 20, 17--56 (2019; Zbl 1436.90099) Full Text: DOI arXiv Link
de Klerk, Etienne; Laurent, Monique; Sun, Zhao Convergence analysis for Lasserre’s measure-based hierarchy of upper bounds for polynomial optimization. (English) Zbl 1358.90092 Math. Program. 162, No. 1-2 (A), 363-392 (2017). MSC: 90C22 90C26 90C30 PDFBibTeX XMLCite \textit{E. de Klerk} et al., Math. Program. 162, No. 1--2 (A), 363--392 (2017; Zbl 1358.90092) Full Text: DOI arXiv Link
De Klerk, Etienne; Laurent, Monique Error bounds for some semidefinite programming approaches to polynomial minimization on the hypercube. (English) Zbl 1229.90279 SIAM J. Optim. 20, No. 6, 3104-3120 (2010). Reviewer: Vladimír Lacko (Košice) MSC: 90C60 90C56 90C26 PDFBibTeX XMLCite \textit{E. De Klerk} and \textit{M. Laurent}, SIAM J. Optim. 20, No. 6, 3104--3120 (2010; Zbl 1229.90279) Full Text: DOI
Laurent, Monique; Mourrain, Bernard A generalized flat extension theorem for moment matrices. (English) Zbl 1183.30030 Arch. Math. 93, No. 1, 87-98 (2009). Reviewer: Gabriel Larotonda (Buenos Aires) MSC: 30E05 12D10 PDFBibTeX XMLCite \textit{M. Laurent} and \textit{B. Mourrain}, Arch. Math. 93, No. 1, 87--98 (2009; Zbl 1183.30030) Full Text: DOI
Lasserre, Jean B.; Laurent, Monique; Rostalski, Philipp A prolongation-projection algorithm for computing the finite real variety of an ideal. (English) Zbl 1172.14036 Theor. Comput. Sci. 410, No. 27-29, 2685-2700 (2009). MSC: 14P05 13J30 13P10 12D99 68W30 90C22 PDFBibTeX XMLCite \textit{J. B. Lasserre} et al., Theor. Comput. Sci. 410, No. 27--29, 2685--2700 (2009; Zbl 1172.14036) Full Text: DOI arXiv
Laurent, Monique Sums of squares, moment matrices and optimization over polynomials. (English) Zbl 1163.13021 Putinar, Mihai (ed.) et al., Emerging applications of algebraic geometry. Papers of the IMA workshops Optimization and control, January 16–20, 2007 and Applications in biology, dynamics, and statistics, March 5–9, 2007, held at IMA, Minneapolis, MN, USA. New York, NY: Springer (ISBN 978-0-387-09685-8/hbk). The IMA Volumes in Mathematics and its Applications 149, 157-270 (2009). Reviewer: Yueh-er Kuo (Knoxville) MSC: 13P10 13J25 14P10 15A99 90C22 90C30 PDFBibTeX XMLCite \textit{M. Laurent}, IMA Vol. Math. Appl. 149, 157--270 (2009; Zbl 1163.13021)
Laurent, Monique Semidefinite programming in combinatorial and polynomial optimization. (English) Zbl 1239.90004 Nieuw Arch. Wiskd. (5) 9, No. 4, 256-262 (2008). MSC: 90-02 90C22 90C27 90C35 PDFBibTeX XMLCite \textit{M. Laurent}, Nieuw Arch. Wiskd. (5) 9, No. 4, 256--262 (2008; Zbl 1239.90004)
Lasserre, Jean Bernard; Laurent, Monique; Rostalski, Philipp Semidefinite characterization and computation of zero-dimensional real radical ideals. (English) Zbl 1176.14010 Found. Comput. Math. 8, No. 5, 607-647 (2008). Reviewer: Alexander Kovačec (Coimbra) MSC: 14P05 13J30 13P10 90C22 65H10 PDFBibTeX XMLCite \textit{J. B. Lasserre} et al., Found. Comput. Math. 8, No. 5, 607--647 (2008; Zbl 1176.14010) Full Text: DOI arXiv
Jibetean, Dorina; Laurent, Monique Semidefinite approximations for global unconstrained polynomial optimization. (English) Zbl 1103.90073 SIAM J. Optim. 16, No. 2, 490-514 (2005). Reviewer: Walter Gómez Bofill (Temuco) MSC: 90C22 90C26 49M20 PDFBibTeX XMLCite \textit{D. Jibetean} and \textit{M. Laurent}, SIAM J. Optim. 16, No. 2, 490--514 (2005; Zbl 1103.90073) Full Text: DOI
Laurent, Monique Revisiting two theorems of Curto and Fialkow on moment matrices. (English) Zbl 1078.14085 Proc. Am. Math. Soc. 133, No. 10, 2965-2976 (2005). Reviewer: Mihai Putinar (Santa Barbara) MSC: 14P10 90C22 47A57 13J30 PDFBibTeX XMLCite \textit{M. Laurent}, Proc. Am. Math. Soc. 133, No. 10, 2965--2976 (2005; Zbl 1078.14085) Full Text: DOI
de Klerk, Etienne; Laurent, Monique; Parillo, Pablo On the equivalence of algebraic approaches to the minimization of forms on the simplex. (English) Zbl 1138.90439 Henrion, Didier (ed.) et al., Positive polynomials in control. Berlin: Springer (ISBN 3-540-23948-0/pbk). Lecture Notes in Control and Information Sciences 312, 121-132 (2005). MSC: 90C22 93B25 PDFBibTeX XMLCite \textit{E. de Klerk} et al., Lect. Notes Control Inf. Sci. 312, 121--132 (2005; Zbl 1138.90439) Full Text: DOI Link