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

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-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 languageEnglish
Title of host publicationWorld Women in Mathematics 2018
Place of PublicationRio de Janeiro
PublisherSpringer
DOIs
Publication statusAccepted/In press - 2019

Publication series

NameAssociation for Women in Mathematics Series
PublisherSpringer
Volume20

Fingerprint

Convex Cone
Semidefinite Programming
Error Analysis
Moment
Outer Approximation
Robust Optimization
Borel Measure
Option Pricing
Approximation
Finance
Quadrature
Rational function
Global Optimization
Numerical integration
Upper and Lower Bounds
Review
Hierarchy

Cite this

de Klerk, E., & Laurent, M. (Accepted/In press). A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis. In World Women in Mathematics 2018 (Association for Women in Mathematics Series ; Vol. 20). Rio de Janeiro: Springer. https://doi.org/10.1007/978-3-030-21170-7_2
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. Rio de Janeiro : Springer, 2019. (Association for Women in Mathematics Series ).
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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 World Women in Mathematics 2018. Association for Women in Mathematics Series , vol. 20, Springer, Rio de Janeiro. https://doi.org/10.1007/978-3-030-21170-7_2

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. Rio de Janeiro : Springer, 2019. (Association for Women in Mathematics Series ; Vol. 20).

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-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 World Women in Mathematics 2018. Rio de Janeiro: Springer. 2019. (Association for Women in Mathematics Series ). https://doi.org/10.1007/978-3-030-21170-7_2