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.
There is a PhD studentship available in related topics, to be supervised by Jakub Marecek and Vyacheslav Kungurtsev (Dept. of Computer Science) and Didier Henrion (Dept. of Control Engineering) at the Czech Technical University, in close collaboration with the teams of Jan Zeman (Department of Mechanics) and Michal Kocvara (School of Mathematics at the University of Birmingham, UK). The position is full time and limited to 3 years, but can be extended in case of mutual interest. The studentship comes with a monthly salary similar to the average pay in Prague, the Czech Republic (approximately 45000 CZK per month before a notably low tax), and a travel budget. The Czech capital regularly ranks among five European cities within the world's best cities in the world to live in (cf. Time Out Magazine index for 2021) and CTU’s offices are in a centrally-located palace with a view of Prague Castle. For more information, please see https://en.wikipedia.org/wiki/Prague
We seek candidates with Masters degrees in Mathematics, Computer Science, Operations Research, Engineering or related disciplines, with excellent mathematical aptitude, as demonstrated by involvement in mathematical olympiads, relevant coursework, or undergraduate research. A preference is given to:
– candidates with experience with semidefinite programming
– candidates with experience with structural engineering
– candidates with experience in frequency-domain methods (e.g. signal processing)
– candidates with experience in programming in Python or MATLAB.
We expect to start interviewing candidates in January 2022. Please leave your email address at https://forms.gle/HC25XBmvopbPkr9F6 or contact Jakub via email at jakub.marecek@fel.cvut.cz.
Czech Technical University (CTU) is the oldest non-military technical university in Europe. In the academic year 2020/21, CTU offered 130 degree programs in Czech and 84 in English. CTU’s control-theory research is well known, especially thanks to Vladimir Kucera. CTU’s Artificial Intelligence Center (AIC) with a staff of 150 is widely recognized as one of the best in the region. Since 1996, Didier Henrion has been affiliated with the Czech Technical University. Since March 2020, Jakub Marecek leads the Optimization research group within the AIC. For more information, please see https://www.aic.fel.cvut.cz/research-areas/optimization
References:
M Tyburec, J Zeman, M Kružík, D Henrion: Global optimality in minimum compliance topology optimization of frames and shells by moment-sum-of-squares hierarchy. Structural and Multidisciplinary Optimization, 2021. https://arxiv.org/pdf/2009.12560.pdf
D Henrion, M Korda, JB Lasserre: Moment-sos Hierarchy, The: Lectures In Probability, Statistics, Computational Geometry, Control And Nonlinear Pdes. World Scientific, 2020.
