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/Conference proceedings/Edited volumeChapterScientificpeer-review

3 Citations (Scopus)

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 publicationAssociation for Women in Mathematics Series
PublisherSpringer
Pages17-56
Number of pages40
DOIs
Publication statusPublished - 2019

Publication series

NameAssociation for Women in Mathematics Series
Volume20
ISSN (Print)2364-5733
ISSN (Electronic)2364-5741

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