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Polynomial Optimization, Efficiency through Moments and Algebra

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.

Coordinator

INSTITUT NATIONAL DE RECHERCHE ENINFORMATIQUE ET AUTOMATIQUE

Address

Domaine De Voluceau Rocquencourt
78153 Le Chesnay Cedex

France

Activity type

Research Organisations

EU Contribution

€ 549 604,08

Participants (10)

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CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS

France

EU Contribution

€ 229 001,70

SORBONNE UNIVERSITE

France

EU Contribution

€ 549 604,08

STICHTING NEDERLANDSE WETENSCHAPPELIJK ONDERZOEK INSTITUTEN

Netherlands

EU Contribution

€ 531 239,76

STICHTING KATHOLIEKE UNIVERSITEIT BRABANT

Netherlands

EU Contribution

€ 265 619,88

UNIVERSITAT KONSTANZ

Germany

EU Contribution

€ 505 576,80

UNIVERSITA DEGLI STUDI DI FIRENZE

Italy

EU Contribution

€ 261 499,68

THE UNIVERSITY OF BIRMINGHAM

United Kingdom

EU Contribution

€ 303 172,56

FRIEDRICH-ALEXANDER-UNIVERSITAET ERLANGEN NUERNBERG

Germany

EU Contribution

€ 252 788,40

UNIVERSITETET I TROMSOE - NORGES ARKTISKE UNIVERSITET

Norway

EU Contribution

€ 292 342,32

ARTELYS

France

EU Contribution

€ 274 802,04

Project information

Grant agreement ID: 813211

Status

Ongoing project

  • Start date

    1 January 2019

  • End date

    31 December 2022

Funded under:

H2020-EU.1.3.1.

  • Overall budget:

    € 4 015 251,30

  • EU contribution

    € 4 015 251,30

Coordinated by:

INSTITUT NATIONAL DE RECHERCHE ENINFORMATIQUE ET AUTOMATIQUE

France