Global weight optimization of frame structures with polynomial programming

0581872 - ÚTIA 2024 RIV DE eng J - Journal Article
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
R&D Projects: GA ČR(CZ) GA22-15524S; GA MŠMT 8J20FR019; GA ČR GF21-06569K
Institutional support: RVO:67985556
Keywords : Topology optimization * Frame structures * Semidefinite programming * Polynomial optimization * Global optimality
OECD category: Applied mathematics
Impact factor: 3.9, year: 2022
Method of publishing: Limited access
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.
Permanent Link: https://hdl.handle.net/11104/0350579