SEMIDEFINITE APPROXIMATIONS OF PROJECTIONS AND POLYNOMIAL IMAGES 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%2F15%3A00233700" target="_blank" >RIV/68407700:21230/15:00233700 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/140992047" target="_blank" >http://dx.doi.org/10.1137/140992047</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/140992047" target="_blank" >10.1137/140992047</a>
Alternative languages
Result language
angličtina
Original language name
SEMIDEFINITE APPROXIMATIONS OF PROJECTIONS AND POLYNOMIAL IMAGES OF SEMIALGEBRAIC SETS
Original language description
Given a compact semialgebraic set S subset of R-n and a polynomial map f : R-n -> R-m, we consider the problem of approximating the image set F = f (S) subset of R-m. This includes in particular the projection of S on R-m for n >= m. Assuming that F subset of B, with B subset of R-m being a "simple" set (e.g., a box or a ball), we provide two methods to compute certified outer approximations of F. Method 1 exploits the fact that F can be defined with an existential quantifier, while Method 2 computes approximations of the support of image measures. The two methods output a sequence of superlevel sets defined with a single polynomial that yield explicit outer approximations of F. Finding the coefficients of this polynomial boils down to computing an optimal solution of a convex semidefinite program. We provide guarantees of strong convergence to F in L-1 norm on B, when the degree of the polynomial approximation tends to infinity. Several examples of applications are provided, together
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM JOURNAL ON OPTIMIZATION
ISSN
1052-6234
e-ISSN
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Volume of the periodical
25
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
22
Pages from-to
2143-2164
UT code for WoS article
000367019700008
EID of the result in the Scopus database
2-s2.0-84953237468