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

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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 languageEnglish
Title of host publicationWorld Women in Mathematics 2018
Subtitle of host publicationProceedings of the First World Meeting for Women in Mathematics (WM)²
EditorsCarolina Araujo, Georgia Benkart, Cheryl E. Praeger, Betül Tanbay
Place of PublicationCham
PublisherSpringer
Pages17-56
ISBN (Print)9783030211691
DOIs
Publication statusPublished - Dec 2019

Publication series

NameAssociation for Women in Mathematics Series
PublisherSpringer
Volume20

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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