Počet záznamů: 1  

Decomposition of arrow type positive semidefinite matrices with application to topology optimization

  1. 1.
    SYSNO ASEP0532970
    Druh ASEPJ - Článek v odborném periodiku
    Zařazení RIVJ - Článek v odborném periodiku
    Poddruh JČlánek ve WOS
    NázevDecomposition of arrow type positive semidefinite matrices with application to topology optimization
    Tvůrce(i) Kočvara, Michal (UTIA-B) RID, ORCID
    Celkový počet autorů1
    Zdroj.dok.Mathematical Programming. - : Springer - ISSN 0025-5610
    Roč. 190, 1-2 (2021), s. 105-134
    Poč.str.30 s.
    Forma vydáníTištěná - P
    Jazyk dok.eng - angličtina
    Země vyd.NL - Nizozemsko
    Klíč. slovasemidefinite optimization ; positive semidefinite matrices ; chordal graphs ; domain decomposition ; topology optimization
    Vědní obor RIVBA - Obecná matematika
    Obor OECDPure mathematics
    Způsob publikováníOpen access
    Institucionální podporaUTIA-B - RVO:67985556
    UT WOS000539869200001
    EID SCOPUS85086374125
    DOI10.1007/s10107-020-01526-w
    AnotaceDecomposition of large matrix inequalities for matrices with chordal sparsity graph has been recently used by Kojima et al. (Math Program 129(1):33–68, 2011) to reduce problem size of large scale semidefinite optimization (SDO) problems and thus increase efficiency of standard SDO software. A by-product of such a decomposition is the introduction of new dense small-size matrix variables. We will show that for arrow type matrices satisfying suitable assumptions, the additional matrix variables have rank one and can thus be replaced by vector variables of the same dimensions. This leads to significant improvement in efficiency of standard SDO software. We will apply this idea to the problem of topology optimization formulated as a large scale linear semidefinite optimization problem. Numerical examples will demonstrate tremendous speed-up in the solution of the decomposed problems, as compared to the original large scale problem. In our numerical example the decomposed problems exhibit linear growth in complexity, compared to the more than cubic growth in the original problem formulation. We will also give a connection of our approach to the standard theory of domain decomposition and show that the additional vector variables are outcomes of the corresponding discrete Steklov–Poincaré operators.
    PracovištěÚstav teorie informace a automatizace
    KontaktMarkéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201.
    Rok sběru2022
    Elektronická adresahttps://link.springer.com/article/10.1007/s10107-020-01526-w
Počet záznamů: 1  

  Tyto stránky využívají soubory cookies, které usnadňují jejich prohlížení. Další informace o tom jak používáme cookies.