### Abstract

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 |
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Title of host publication | World Women in Mathematics 2018 |

Place of Publication | Rio de Janeiro |

Publisher | Springer |

DOIs | |

Publication status | Accepted/In press - 2019 |

### Publication series

Name | Association for Women in Mathematics Series |
---|---|

Publisher | Springer |

Volume | 20 |

### Fingerprint

### Cite this

*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

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*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.

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

TY - CHAP

T1 - A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis

AU - de Klerk, Etienne

AU - Laurent, Monique

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-030-21170-7_2

DO - 10.1007/978-3-030-21170-7_2

M3 - Chapter

T3 - Association for Women in Mathematics Series

BT - World Women in Mathematics 2018

PB - Springer

CY - Rio de Janeiro

ER -