0581872 20250131152608.920240125235959.9 85179724837 001124449100003 10.1007/s00158-023-03715-5 10 s. P cav_un_epca*02557351615-147X66 Topology optimization Frame structures Semidefinite programming Polynomial optimization Global optimality cav_un_auth*0454762 Tyburec Marek UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR CZ 50 K Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0101131 Kočvara Michal UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR 30 Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0101142 Kružík Martin UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR 20 Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2024/MTR/tyburec-0581872.pdf https://link.springer.com/article/10.1007/s00158-023-03715-5 GA22-15524S GA ČR CZ cav_un_auth*0447354 8J20FR019 GA MŠk cav_un_auth*0397550 GF21-06569K GA ČR cav_un_auth*0412957 Weight optimization of frame structures with continuous cross-section parametrization is a challenging non-convex problem that has traditionally been solved by local optimization techniques. Here, we exploit its inherent semi-algebraic structure and adopt the Lasserre hierarchy of relaxations to compute the global minimizers. While this hierarchy generates a natural sequence of lower bounds, we show, under mild assumptions, how to project the relaxed solutions onto the feasible set of the original problem and thus construct feasible upper bounds. Based on these bounds, we develop a simple sufficient condition of global Ɛ-optimality. Finally, we prove that the optimality gap converges to zero in the limit if the set of global minimizers is convex. We demonstrate these results by means of two academic illustrations. WOS BA 10000 10100 10102 2024 3 RVO:67985556 https://hdl.handle.net/11104/0350579 cav_un_auth*0300409 České vysoké učení technické v Praze, Fakulta stavební ČVUT Praha, FSv CZ cav_un_auth*0297783 University of Birmingham GB S 257 Article Computer Science Interdisciplinary Applications|Engineering Multidisciplinary|Mechanics C ENGINEERING.MULTIDISCIPLINARY|MECHANICS|COMPUTERSCIENCE.INTERDISCIPLINARYAPPLICATIONS 4.1 1.1 6.6 0.013 0.958 15057 147 1.181 48.84 4.01 4631 Q1 3.100 253 Q1 76.7 Q2 Q2 0.97 Q1 83.1 2023 85179724837 SCOPUS PUBMED 001124449100003 WOS cav_un_epca*0255735 Structural and Multidisciplinary Optimization 66 12 2023 1615-147X 1615-1488