A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis

Etienne de Klerk; Monique Laurent

doi:10.1007/978-3-030-21170-7_1

A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis

Etienne de Klerk, Monique Laurent

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Scientific › peer-review

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Abstract

The generalized problem of moments is a conic linear optimization
problem over the convex cone of positive Borel measures with given support. It
has a large variety of applications, including global optimization of polynomials
and rational functions, option pricing in finance, constructing quadrature schemes
for numerical integration, and distributionally robust optimization. A usual solution
approach, due to J.B. Lasserre, is to approximate the convex cone of positive
Borel measures by finite dimensional outer and inner conic approximations. We
will review some results on these approximations, with a special focus on the
convergence rate of the hierarchies of upper and lower bounds for the general
problem of moments that are obtained from these inner and outer approximations.

Original language	English
Title of host publication	World Women in Mathematics 2018
Subtitle of host publication	Proceedings of the First World Meeting for Women in Mathematics (WM)²
Editors	Carolina Araujo, Georgia Benkart, Cheryl E. Praeger, Betül Tanbay
Place of Publication	Cham
Publisher	Springer
Pages	17-56
ISBN (Print)	9783030211691
DOIs	https://doi.org/10.1007/978-3-030-21170-7_1
Publication status	Published - Dec 2019

Publication series

Name	Association for Women in Mathematics Series
Publisher	Springer
Volume	20

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10.1007/978-3-030-21170-7_1

AWM_survey_proofsProof, 720 KBLicence: Unspecified

Cite this

de Klerk, E., & Laurent, M. (2019). A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis. In C. Araujo, G. Benkart, C. E. Praeger, & B. Tanbay (Eds.), World Women in Mathematics 2018: Proceedings of the First World Meeting for Women in Mathematics (WM)² (pp. 17-56). (Association for Women in Mathematics Series ; Vol. 20). Springer. https://doi.org/10.1007/978-3-030-21170-7_1

de Klerk, Etienne ; Laurent, Monique. / A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis. World Women in Mathematics 2018: Proceedings of the First World Meeting for Women in Mathematics (WM)². editor / Carolina Araujo ; Georgia Benkart ; Cheryl E. Praeger ; Betül Tanbay. Cham : Springer, 2019. pp. 17-56 (Association for Women in Mathematics Series ).

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abstract = "The generalized problem of moments is a conic linear optimizationproblem over the convex cone of positive Borel measures with given support. Ithas a large variety of applications, including global optimization of polynomialsand rational functions, option pricing in finance, constructing quadrature schemesfor numerical integration, and distributionally robust optimization. A usual solutionapproach, due to J.B. Lasserre, is to approximate the convex cone of positiveBorel measures by finite dimensional outer and inner conic approximations. Wewill review some results on these approximations, with a special focus on theconvergence rate of the hierarchies of upper and lower bounds for the generalproblem of moments that are obtained from these inner and outer approximations.",

author = "{de Klerk}, Etienne and Monique Laurent",

note = "The file Erratum-Theorem9-GMP-survey.pdf contains an erratum to Theorem 9 in the chapter.",

year = "2019",

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doi = "10.1007/978-3-030-21170-7_1",

language = "English",

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booktitle = "World Women in Mathematics 2018",

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de Klerk, E & Laurent, M 2019, A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis. in C Araujo, G Benkart, CE Praeger & B Tanbay (eds), World Women in Mathematics 2018: Proceedings of the First World Meeting for Women in Mathematics (WM)². Association for Women in Mathematics Series , vol. 20, Springer, Cham, pp. 17-56. https://doi.org/10.1007/978-3-030-21170-7_1

A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis. / de Klerk, Etienne ; Laurent, Monique.
World Women in Mathematics 2018: Proceedings of the First World Meeting for Women in Mathematics (WM)². ed. / Carolina Araujo; Georgia Benkart; Cheryl E. Praeger; Betül Tanbay. Cham: Springer, 2019. p. 17-56 (Association for Women in Mathematics Series ; Vol. 20).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Scientific › peer-review

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de Klerk E , Laurent M. A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis. In Araujo C, Benkart G, Praeger CE, Tanbay B, editors, World Women in Mathematics 2018: Proceedings of the First World Meeting for Women in Mathematics (WM)². Cham: Springer. 2019. p. 17-56. (Association for Women in Mathematics Series ). doi: 10.1007/978-3-030-21170-7_1

A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis

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