Convergence rates of moment-sum-of-squares hierarchies for volume approximation of semialgebraic sets
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F18%3A00324699" target="_blank" >RIV/68407700:21230/18:00324699 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s11590-017-1186-x" target="_blank" >http://dx.doi.org/10.1007/s11590-017-1186-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11590-017-1186-x" target="_blank" >10.1007/s11590-017-1186-x</a>
Alternative languages
Result language
angličtina
Original language name
Convergence rates of moment-sum-of-squares hierarchies for volume approximation of semialgebraic sets
Original language description
Moment-sum-of-squares hierarchies of semidefinite programs can be used to approximate the volume of a given compact basic semialgebraic set K. The idea consists of approximating from above the indicator function of K with a sequence of polynomials of increasing degree d, so that the integrals of these polynomials generate a convergence sequence of upper bounds on the volume of K. Under certain assumptions, we show that the asymptotic rate of this convergence is at least O(1/log log d) in general and O(1/log d) provided that the semialgebraic set is defined by a single inequality.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Optimization Letters
ISSN
1862-4472
e-ISSN
1862-4480
Volume of the periodical
12
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
8
Pages from-to
435-442
UT code for WoS article
000429677700001
EID of the result in the Scopus database
2-s2.0-85029461112