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POEMA project : Polynomial Optimization, Efficiency through Moments and Algebra

Coordinated by the AROMATH research team headed by Bernard Mourrain (Inria Sophia Antipolis), the POEMA project is a European (H2020) Training Network designed to go beyond traditional paradigms of Mathematical optimization by exploiting new advances in algebra and convex geometry. Mathematical optimization yields significant advantages for many industry and society sectors, ranging from production planning processes, transportation, to energy consumption, and resources control, where optimization solutions are used to determine the behaviour of many devices or services.

The challenge addressed by POEMA is to build a new generation of robust global optimization methods. To that end the project will focus on Polynomial Optimisation Problems (POP), as polynomial functions are extensively used in optimization and more generally for modelling in science and engineering.

In that perspective, the core academic partner of POEMA, namely Inria, CNRSSUCWI,UvTUKONUNIFIUoBFAU, UiT, will train 15 early-stage researchers  in these emerging techniques, which involve strong competencies across different domains and skill development.

This should result in the creation of a community of experts in Global Polynomial Optimization at the European level, bringing this new area steps further and increasing its impact on society at large.

And as this community develops and gains both academic expertise and industrial insight, it will reinforce strategic connections between research and industry. Industry professionals, and POEMA industrial partners (ARTELYS, IBM, NAG, RTE), expect the application of such techniques to play a major role in upcoming technological developments.

The POEMA initiative will therefore implement an advanced training programme addressing both academic and industrial agenda, focusing on:

  • New advances in the analysis and in the understanding of the algebra and geometry involved in polynomial optimization problems, which lead to significant progress in the development of new efficient algorithms and implementations for solving global optimization problems.
  • New, alternative methods for solving global optimization problems, exploiting the structure of the problems for efficiency and accuracy. An industrial breakthrough should be a new class of optimization software that can solve real life global optimisation problems.
  • Developing the scope of applications of this new paradigm by addressing challenging applications and optimization bottlenecks in physics, information processing, communication, economy, energy management, etc… opening new innovation perspectives across numerous domains.

Keywords: Polynomial optimization Robust global optimization methods Polynomial functions Algebra Industrial partners Applications Energy management Economy

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