0532970 20240103224520.620201012235959.9 85086374125 000539869200001 10.1007/s10107-020-01526-w 30 s. P cav_un_epca*02572270025-5610190105-134Springer semidefinite optimization positive semidefinite matrices chordal graphs domain decomposition topology optimization cav_un_auth*0101131 Kočvara Michal UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory 100 Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2020/MTR/kocvara-0532970.pdf https://link.springer.com/article/10.1007/s10107-020-01526-w Decomposition 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. WOS BA 10000 10100 10101 2022 1 RVO:67985556 http://hdl.handle.net/11104/0311548 S 2 Article Computer Science Software Engineering|Operations Research Management Science|Mathematics Applied A OPERATIONSRESEARCH&MANAGEMENTSCIENCE|MATHEMATICS.APPLIED|COMPUTERSCIENCE.SOFTWAREENGINEERING 4.268 0.745 15.5 0.01577 2.577 13781 149 2.794 35.88 3.51 1385 Q1 2.745 165 Q1 73 Q1* Q1* 1.28 Q1 90.075 2021 85086374125 SCOPUS PUBMED 000539869200001 WOS cav_un_epca*0257227 Mathematical Programming 0025-5610 1436-4646 Roč. 190 1-2 2021 105 134 Springer