Global weight optimization of frame structures with polynomial programming

0581872 - ÚTIA 2024 RIV DE eng J - Článek v odborném periodiku
Tyburec, Marek - Kočvara, Michal - Kružík, Martin
Global weight optimization of frame structures with polynomial programming.
Structural and Multidisciplinary Optimization. Roč. 66, č. 12 (2023), č. článku 257. ISSN 1615-147X. E-ISSN 1615-1488
Grant CEP: GA ČR(CZ) GA22-15524S; GA MŠMT 8J20FR019; GA ČR GF21-06569K
Institucionální podpora: RVO:67985556
Klíčová slova: Topology optimization * Frame structures * Semidefinite programming * Polynomial optimization * Global optimality
Obor OECD: Applied mathematics
Impakt faktor: 3.9, rok: 2022
Způsob publikování: Omezený přístup
http://library.utia.cas.cz/separaty/2024/MTR/tyburec-0581872.pdf https://link.springer.com/article/10.1007/s00158-023-03715-5

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.
Trvalý link: https://hdl.handle.net/11104/0350579