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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 book chapters deposited in this HAL collection are the author's versions (preprint).

Table of Contents


Polynomial Optimization, Moments, and Applications
Michal Kočvara, Bernard Mourrain, Cordian Riener

Introduction
Polynomial Optimization, Certificates of Positivity, and Christoffel Function
Jean-Bernard Lasserre

1-20
Relative entropy methods in constrained polynomial and signomial optimization
Thorsten Theobald

21-46
Symmetries in polynomial optimization
Philippe Moustrou, Cordian Riener, Hugues Verdure

47-98
Copositive matrices, sums of squares and the stability number of a graph
Luis Felipe Vargas, Monique Laurent

99-132
Matrix factorization ranks via polynomial optimization
Andries Steenkamp

135-162
Polynomial optimization in geometric modeling
Soodeh Habibi, Michal Kočvara, Bernard Mourrain

163-186
Assessing Safety for Control Systems Using Sum-of-Squares Programming
Han Wang, Kostas Margellos, Antonis Papachristodoulou

187-214
Polynomial Equations: Theory and Practice
Simon Telen

215-240

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  Funding from the European Union’s Horizon 2020
research and innovation programme under the Marie Skłodowska-Curie
grant agreement N° 813211  (POEMA)