Polynomial optimization is an exciting area of research in optimization, just at the boundary between what is undecidable and what is efficiently solvable. Sustained progress in the field over the past two decades has enabled new applications within many areas of engineering. One novel application arises in structural engineering.
Polynomial optimization is an exciting area of research in optimization, just at the boundary between what is undecidable (continuous optimization) and what is efficiently solvable (easier conic optimization problems, such as linear and semidefinite programming). Sustained progress in the field over the past two decades has enabled new applications within many areas of engineering.
One novel application arises in structural engineering. There, thin frame and shell theories have been successfully used in diverse applications encompassing, e.g., the construction of the Eiffel tower and wind-turbine towers. Designing such structures for optimal mechanical performance is notoriously challenging because of the inherent non-convexity of the resulting optimization problems. A certain static minimum-compliance problem can be cast as a polynomial optimization program, which in turn, can be solved to the guaranteed global optimality by a hierarchy of convexifications. This opens entirely new avenues in the optimal design of bending-resistant structures that we wish to explore in the current project in the context of structural dynamics.
A multi-disciplinary team including Jakub Marecek, Vyacheslav Kungurtsev (Dept. of Computer Science), Didier Henrion (Dept. of Control Engineering), Jan Zeman and Marek Tyburec (Department of Mechanics) at the Czech Technical University, Jiri Outrata (Czech Academy of Sciences), and Michal Kocvara (School of Mathematics at the University of Birmingham, UK) received funding for related work for 2022-2024 from the Czech Science Foundation (GACR) under award number 22-15524S.
Image credit: Jan Zeman and Marek Tyburec.
