[Opt-Net] PhD Position: Polynomial Optimization in Structural Engineering

[marecjak at fel.cvut.cz]

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.

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.