Convergence rates for sums-of-squares hierarchies with correlative sparsity
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00374755" target="_blank" >RIV/68407700:21230/25:00374755 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10107-024-02071-6" target="_blank" >https://doi.org/10.1007/s10107-024-02071-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10107-024-02071-6" target="_blank" >10.1007/s10107-024-02071-6</a>
Alternative languages
Result language
angličtina
Original language name
Convergence rates for sums-of-squares hierarchies with correlative sparsity
Original language description
This work derives upper bounds on the convergence rate of the moment-sum-of-squares hierarchy with correlative sparsity for global minimization of polynomials on compact basic semialgebraic sets. The main conclusion is that both sparse hierarchies based on the Schmudgen and Putinar Positivstellensatze enjoy a polynomial rate of convergence that depends on the size of the largest clique in the sparsity graph but not on the ambient dimension. Interestingly, the sparse bounds outperform the best currently available bounds for the dense hierarchy when the maximum clique size is sufficiently small compared to the ambient dimension and the performance is measured by the running time of an interior point method required to obtain a bound on the global minimum of a given accuracy.
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
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/EH22_008%2F0004590" target="_blank" >EH22_008/0004590: Robotics and advanced industrial production</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical Programming
ISSN
0025-5610
e-ISSN
1436-4646
Volume of the periodical
209
Issue of the periodical within the volume
1-2
Country of publishing house
DE - GERMANY
Number of pages
39
Pages from-to
435-473
UT code for WoS article
001190454600001
EID of the result in the Scopus database
2-s2.0-85183794961