Geometry of exactness of moment-SOS relaxations for polynomial optimization
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00383696" target="_blank" >RIV/68407700:21230/25:00383696 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s11590-025-02202-8" target="_blank" >https://doi.org/10.1007/s11590-025-02202-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11590-025-02202-8" target="_blank" >10.1007/s11590-025-02202-8</a>
Alternative languages
Result language
angličtina
Original language name
Geometry of exactness of moment-SOS relaxations for polynomial optimization
Original language description
The moment-SOS (sum of squares) hierarchy is a powerful approach for solving approximately and globally non-convex polynomial optimization problems (POPs) at the price of solving a family of convex semidefinite optimization problems (called moment-SOS relaxations) of increasing size, controlled by an integer, the relaxation order. We say that a relaxation of a given order is exact if solving the relaxation actually solves the POP globally. In this note, we study the geometry of the exactness cone, defined as the set of polynomial objective functions for which the relaxation is exact. Generalizing previous foundational work on quadratic optimization on real varieties, we prove by elementary arguments that the exactness cones are unions of semidefinite representable cones monotonically embedded for increasing relaxation order.
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
Optimization Letters
ISSN
1862-4472
e-ISSN
1862-4480
Volume of the periodical
19
Issue of the periodical within the volume
6
Country of publishing house
DE - GERMANY
Number of pages
10
Pages from-to
1239-1248
UT code for WoS article
001484444800001
EID of the result in the Scopus database
2-s2.0-105004438835