SEMIDEFINITE APPROXIMATIONS OF PROJECTIONS AND POLYNOMIAL IMAGES OF SEMIALGEBRAIC SETS

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

SEMIDEFINITE APPROXIMATIONS OF PROJECTIONS AND POLYNOMIAL IMAGES OF SEMIALGEBRAIC SETS

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

SEMIDEFINITE APPROXIMATIONS OF PROJECTIONS AND POLYNOMIAL IMAGES OF SEMIALGEBRAIC SETS

Popis výsledku anglicky

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

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

SIAM JOURNAL ON OPTIMIZATION

ISSN

1052-6234

e-ISSN

—

Svazek periodika

25

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

2143-2164

Kód UT WoS článku

000367019700008

EID výsledku v databázi Scopus

2-s2.0-84953237468