The successful campaign of recruitment of 15 ESRs leads to the constitution of a task force of young and talented researchers during the first year of the project. Thanks to a large communication on the PhD positions available in POEMA through various channels including academic networks, social networks, mailing lists in our community, etc, we received an impressive number of applications (more than 230). A strong review and selection process was organized by the position committee, with interviews taking place online and at the kick-off meeting.
New research in polynomial optimization has been developed inside the network. After the ESRs started investigating their subjects during the second year of the project, they all have produce new results in the area of algebraic computation for moments, mix-integer nonlinear programming, structure and robustness and applications as assessed by the publication accepted or submitted for publication. The important number of publications acknowledging POEMA support also shows the extreme vitality of the research activities of the network members.
During the project, significant advances have been made in particular by the ESRs and the other network members on exact representations of positive polynomials by Sum of Square, on the power of approximations of the moment and SOS hierachies, on the exploitation of symmetries and sparsity in polynomial optimization, on the extension of polynomial optimization in graph problems and copositive matrices, on the use of moment-sum-of-squares hierarchies for analysing solutions of dynamical systems and partial differential equations. Applications of these works have been developed in Optimal Power Flow problems, in finance, in geometric modeling, structural mechanics and truss topology optimization, VSLI design, the analysis of biological data and of protein interactions. Thanks to theses methodological progresses, problems which were previously unattainable fall now within the realm of feasible polynomial optimization problems.
The network POEMA also contributed to software developments, with the production of dedicated packages such as MomentTools, TSSOS, Loraine (in Julia) for polynomial optimization or msolve (in C) for finding the roots of polynomial equations.
The training and networking events have been organized as closely as possible to the initial plan. The kick-off meeting and first workshop took place on site and the first learning week, second and third workshops happened online. The international visibility of POEMA network in the community is very high. The ESRs are strongly involved and contributing to this success. We organized a very successful final conference, with excellent invited talks, very good presentations of the ESRs and an important attendance of and contributions from the members of the network and experts outside the network.
At this time, most of the PhD have defended successfully and the young PhDs are now either working in the academic sector as post-doctorate in order to pursue a career in research or working for government bodies or in industrial sectors such as financial technology.
