This is the collection of chapters of POEMA book, presenting research activities related to the European Network POEMA, dedicated to polynomial and moment optimization. This project receives funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement N° 813211 (POEMA).

The content of POEMA Book contains 8 chapters:

  • Polynomial Optimization, Certificates of Positivity, and Christoffel Function - Jean-Bernard Lasserre
  • Relative entropy methods in constrained polynomial and signomial optimization - Thorsten Theobald
  • Symmetries in polynomial optimization - Philippe Moustrou, Cordian Riener, Hugues Verdure
  • Copositive matrices, sums of squares and the stability number of a graph - Luis Felipe Vargas, Monique Laurent
  • Matrix factorization ranks via polynomial optimization - Andries Steenkamp
  • Polynomial optimization in geometric modeling - Soodeh Habibi, Michal Kočvara, Bernard Mourrain
  • Assessing Safety for Control Systems Using Sum-of-Squares Programming - Han Wang, Kostas Margellos, Antonis Papachristodoulou
  • Polynomial Equations: Theory and Practice - Simon Telen

The book chapters deposited in this HAL collection are the author's versions (preprint): https://inria.hal.science/POEMA-BOOK/