POEMA - Polynomial Optimization, Efficiency through Moments and Algebra

Marie Skłodowska-Curie Innovative Training Network (2019-2022)

Coordinator of the POEMA consortium: Bernard Mourrain (bernard.mourrain@inria.fr)

Site leader at CWI: Monique Laurent (M.Laurent@cwi.nl)

The consortium POEMA consists of 14 partners in six European countries, inclusing CWI, Amsterdam, and Tilburg University in the Netherlands, and 3 associate partners. See also Cordis for details.

The consortium has 15 PhD positions in total. Among them there are two PhD positions available at CWI from September 2019. Descriptions of these two positions can be found below:

(ESR 6) Approximation hierarchies for (non-)commutative polynomial optimization

(ESR 7) Approximation hierarchies for graph parameters

For details on how to apply, see here. The deadline for applying is 15 March 2019.

For information about these two positions please contact Monique Laurent.

As background material about the research topic you may take a look at the following papers and further papers referenced there.

About polynomial optimization:

J.B. Lasserre. Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11, 796-817 (2001).

E. de Klerk and M. Laurent. A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis. arXiv.

M. Laurent. Sums of squares, moment matrices and optimization over polynomials. In Emerging Applications of Algebraic Geometry, Vol. 149 of IMA Volumes in Mathematics and its Applications, 2009. File.

About conic and non-commutative polynomial optimization and applications to matrix factorization ranks and quantum information:

S. Gribling, D. de Laat, M. Laurent. Lower bounds on matrix factorization ranks via noncommutative polynomial optimization. Foundations of Computational Mathematics, 2019. arXiv.

S. Gribling, D. de Laat, M. Laurent. Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization. Mathematical Programming, 2018. Paper.

M. Laurent, T. Piovesan. Conic approach to quantum graph parameters using linear optimization over the completely positive semidefinite cone. SIAM Journal on Optimization, 2015. arXiv.