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Moment approximations for set-semidefinite polynomials
Dickinson, Peter J. C. (Avtor), Povh, Janez (Avtor)

URLURL - Predstavitvena datoteka, za dostop obiščite http://link.springer.com/article/10.1007/s10957-013-0279-7/fulltext.html Povezava se odpre v novem oknu

Izvleček
The set of polynomials that are nonnegative over a subset of the nonnegative orthant (we call them set-semidefinite) have many uses in optimization. A common example of this type set is the set of copositive matrices, where we are effectively considering nonnegativity over the entire nonnegative orthant and are restricted to homogeneous polynomials of degree two. Lasserre (SIAM J. Optim., 21(3):864885, 2011) has previously considered a method using moments in order to provide an outer approximation to this set, for nonnegativity over a general subset of the real space. In this paper, we shall show that, in the special case of considering nonnegativity over a subset of the nonnegative orthant, we can provide a new outer approximation hierarchy. This is based on restricting moment matrices to be completely positive, and it is at least as good as Lasserres method. This can then be relaxed to give tractable approximations that are still at least as good as Lasserres method. In doing this, we also provide interesting new insights into the use of moments in constructing these approximations.

Jezik:Angleški jezik
Ključne besede:nonnegative polynomials, set-semidefinite polynomials, copositive programming, Doubly nonnegative matrices, Moments, Completely positive matrices
Vrsta gradiva:Delo ni kategorizirano (r6)
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:NTF - Naravoslovnotehniška fakulteta
Leto izida:2013
Št. strani:str. 57-68
Številčenje:Vol. 159, issue 1
UDK:519.6
ISSN pri članku:1573-2878
DOI:10.1007/s10957-013-0279-7 Povezava se odpre v novem oknu
COBISS.SI-ID:2048193299 Povezava se odpre v novem oknu
Število ogledov:599
Število prenosov:259
Metapodatki:XML RDF-CHPDL DC-XML DC-RDF
 
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Gradivo je del revije

Naslov:Journal of optimization theory and applications
Skrajšan naslov:J. optim. theory appl.
Založnik:Kluwer
ISSN:1573-2878
COBISS.SI-ID:513199641 Povezava se odpre v novem oknu

Sekundarni jezik

Jezik:Angleški jezik
Ključne besede:nenegativni polinomi, pogojno pozitivni polinomi, kopozitivno programiranje, dvojno nenegativne matrike, momenti, popolnoma pozitivne matrike

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