Projet POEMA (Horizon 2020, appel à projets 2018)
Action : Doctoral Networks
Panel : Mathematics
Statut du projet : SIGNED

Non-linear optimization problems are present in many real-life applications and in scientific areas such as operations research, control engineering, physics, information processing, economy, biology, etc. However, efficient computational procedures, that can provide the guaranteed global optimum, are lacking for them. The project will develop new polynomial optimization methods, combining moment relaxation procedures with computational algebraic tools to address this type of problems. Recent advances in mathematical programming have shown that the polynomial optimization problems can be approximated by sequences of Semi-Definite Programming problems. This approach provides a powerful way to compute global solutions of non-linear optimization problems and to guarantee the quality of computational results. On the other hand, advanced algebraic algorithms to compute all the solutions of polynomial systems, with efficient implementations for exact and approximate solutions, were developed in the past twenty years. The network combines the expertise of active European teams working in these two domains to address important challenges in polynomial optimization and to show the impact of this research on practical applications. The network will train a new squad of 15 young researchers to master high-level mathematics, algorithm design, scientific computation and software development, and to solve optimization problems for real-world applications. It will advance the research on algebraic methods for moment approaches, tackle mixed integer non-linear optimization problems and enhance the efficiency and robustness of moment relaxation methods. Specific applications of these approaches to optimization problems are related to smarter cities challenges, such as water distribution network management, energy flow in power systems, urban traffic management, as well as to oceanography and environmental monitoring and finance.

Mots clés : optimization, semi definite programming, convex algebraic geometry, polynomial constraints, moments, sum of squares, real algebraic geometry

Participants :
- University of Erlangen-Nuremberg (Allemagne) — Partner, beneficiary, Enseignement supérieur ou secondaire, subvention : 252788.4 €
- Artelys (France) — Partner, beneficiary, Organismes privés (hors enseignement), subvention : 229001.7 €
- Centre national de la recherche scientifique (France) — Partner, beneficiary, Recherche, subvention : 274802.04 €
- Institut national de recherche en sciences et technologies du numérique (France) — Coordinator, beneficiary, Recherche, subvention : 549604.08 €
- University of Konstanz (Allemagne) — Partner, beneficiary, Enseignement supérieur ou secondaire, subvention : 505576.8 €
- Dutch Research Council (Pays-Bas) — Partner, beneficiary, Recherche, subvention : 531239.76 €
- University of Birmingham (Royaume-Uni) — Partner, beneficiary, Enseignement supérieur ou secondaire, subvention : 303172.56 €
- UiT The Arctic University of Norway (Norvège) — Partner, beneficiary, Enseignement supérieur ou secondaire, subvention : 292342.32 €
- Sorbonne Université (France) — Partner, beneficiary, Enseignement supérieur ou secondaire, subvention : 549604.08 €
- University of Florence (Italie) — Partner, beneficiary, Enseignement supérieur ou secondaire, subvention : 261499.68 €
- Tilburg University (Pays-Bas) — Partner, beneficiary, Enseignement supérieur ou secondaire, subvention : 265619.88 €