Keywords

  • Real algebraic geometry
  • Computer algebra
  • Polynomial optimization, semidefinite and hyperbolic programming
  • Nonnegative polynomials and sums of squares

Research interests

My work is in computer algebra, polynomial optimization and real algebraic geometry, and on possible interactions between these disciplines. In my PhD thesis I worked on a symbolic computational approach to linear matrix inequalities and semidefinite programming.

Publications [arXiv list]

2017

  • Solving rank-constrained semidefinite programs in exact arithmetic. Journal of Symbolic Computation (2017) [PDF] [online]. Conference version of this paper published in the Proceedings of ISSAC 2016.
  • D. Henrion, S. Naldi, M. Safey El Din. SPECTRA - A Maple library for solving linear matrix inequalities in exact arithmetic. [arxiv] [online]. Optimization Methods and Software (2017).

2016

  • D. Henrion, S. Naldi, M. Safey El Din. Exact algorithms for linear matrix inequalities. SIAM J. on Optimization, 26(4):2512--2539 (2016) [PDF] [online]
  • Solving rank-constrained semidefinite programs in exact arithmetic. Proceedings of the 41st International Symposium on Symbolic and Algebraic Computation, Waterloo ON (2016) [PDF] [online]. Extended version of this paper published in the Journal of Symbolic Computation.
  • D. Henrion, S. Naldi, M. Safey El Din. Real root finding for determinants of linear matrices. Journal of Symbolic Computation, 74:205--238 (2016) [PDF] [online]

2015

  • D. Henrion, S. Naldi, M. Safey El Din. Real root finding for rank defects in linear Hankel matrices. Proceedings of the 40th International Symposium on Symbolic and Algebraic Computation, Bath UK (2015) [PDF] [online]

2014

  • Nonnegative polynomials and their Carathéodory number. Discrete and Computational Geometry, 51(3):559--568 (2014). [PDF] [online]

Preprints

  • S. Naldi, D. Plaumann. Symbolic computation in hyperbolic programming. Submitted. [arxiv]. Accepted for oral presentation at MEGA 2017, Nice, 12-16 June 2017.
  • D. Henrion, S. Naldi, M. Safey El Din. Real root finding for low rank linear matrices. Submitted. [arxiv]

Theses

  • PhD Thesis (2015): Exact algorithms for determinantal varieties and semidefinite programming. University of Toulouse, France, September 2015. [HAL]
  • Master's Degree Thesis (2012): Extremal decompositions of nonnegative polynomials and the Carathéodory number. University of Florence, Italy, April 2012. [LINK]