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H2020Doctoral network2019–2023

POEMA · Polynomial Optimization, Efficiency through Moments and Algebra

Horizon 2020 — Marie Skłodowska-Curie Actions

Duration
2019-01-01 → 2023-06-30
EU contribution
€4,015,251
Participants
11
Scheme
MSCA-ITN

Lines connect the coordinator with its partners.

Results in brief

Polynomial Optimization, Efficiency through Moments and Algebra

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 aims to develop new polynomial optimization methods, combining moment relaxation procedures with computational algebraic tools to address this type of problems. Recent advances in mathematical programming and computer algebra have shown that the polynomial optimization problems can be approximated by sequences of Semi-Definite Programming problems, which provides a powerful way to compute global solutions of non-linear optimization problems and to guarantee the quality of computational results. Advanced algebraic algorithms allow to compute all the solutions of polynomial systems, with efficient implementations for exact and approximate solutions, were developed in the past twenty years. Combining the expertise of active European teams working in these domains, the project has targeted important challenges in polynomial optimization and demonstrating the impact of this research on practical applications such as water distribution network management, energy flow in power systems, urban traffic management, oceanography and environmental monitoring and finance. The network has trained successfully 15 young researchers to master high-level mathematics, algorithm design, scientific computation and software development, and to solve optimization problems for real-world applications.

Data: CORDIS, © European Union

Project objective

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.

Original text from CORDIS.

Participants

  • INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE · Le Chesnay CedexCoordinatorFrance
  • ARTELYS · ParisFrance
  • CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS · ParisFrance
  • FRIEDRICH-ALEXANDER-UNIVERSITAET ERLANGEN-NUERNBERG · ErlangenGermany
  • SORBONNE UNIVERSITE · ParisFrance
  • STICHTING NEDERLANDSE WETENSCHAPPELIJK ONDERZOEK INSTITUTEN · UtrechtNetherlands
  • THE UNIVERSITY OF BIRMINGHAM · BirminghamUnited Kingdom
  • TILBURG UNIVERSITY- UNIVERSITEIT VAN TILBURG · TilburgNetherlands
  • UNIVERSITA DEGLI STUDI DI FIRENZE · FlorenceItaly
  • UNIVERSITAT KONSTANZ · KonstanzGermany
  • UNIVERSITETET I TROMSOE - NORGES ARKTISKE UNIVERSITET · TromsoNorway

Links

Data: CORDIS, © European Union