, Long and winding central paths, arXiv preprint, 2014.
, Solving generic nonarchimedean semidefinite programs using stochastic game algorithms, Proceedings of ISSAC 2016, 2016.
DOI : 10.1016/j.jsc.2017.07.002
URL : https://hal.archives-ouvertes.fr/hal-01429021
, Mosek: High performance software for large-scale lp, qp, socp, sdp and mip, 2013.
, Introduction to semidefinite, conic and polynomial optimization, in Handbook on semidefinite, conic and polynomial optimization, pp.1-22, 2012.
, Intrinsic complexity estimates in polynomial optimization, Journal of Complexity, vol.30, issue.4, p.pp. ?, 2014.
DOI : 10.1016/j.jco.2014.02.005
URL : https://hal.archives-ouvertes.fr/hal-00815123
, A new algorithm to find a point in every cell defined by a family of polynomials, in Quantifier elimination and cylindrical algebraic decomposition, Algorithms in real algebraic geometry, 1998.
, Nonnegative polynomials and sums of squares, Journal of the American Mathematical Society, vol.25, issue.3, pp.617-635, 2012.
DOI : 10.1090/S0894-0347-2012-00733-4
, Semidefinite optimization and convex algebraic geometry, 2013.
DOI : 10.1137/1.9781611972290
, Bifurcations and catastrophes: geometry of solutions to nonlinear problems, 2013.
DOI : 10.1007/978-3-642-57134-3
, A Gr??bner Free Alternative for Polynomial System Solving, Journal of Complexity, vol.17, issue.1, pp.154-211, 2001.
DOI : 10.1006/jcom.2000.0571
, Computing rational solutions of linear matrix inequalities, Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation, ISSAC '13, pp.197-204, 2013.
DOI : 10.1145/2465506.2465949
URL : https://hal.archives-ouvertes.fr/hal-00815174
, On the Convergence of the Central Path in Semidefinite Optimization, SIAM Journal on Optimization, vol.12, issue.4, pp.1090-1099, 2002.
DOI : 10.1137/S1052623401390793
, Real root finding for determinants of linear matrices, Journal of Symbolic Computation, vol.74, pp.205-238, 2015.
DOI : 10.1016/j.jsc.2015.06.010
URL : https://hal.archives-ouvertes.fr/hal-01077888
, Improving root separation bounds, Journal of Symbolic Computation, vol.84, 2017.
DOI : 10.1016/j.jsc.2017.03.001
URL : https://hal.archives-ouvertes.fr/hal-01456686
, Implementation and Performance Evaluation of an Extended Precision Floating-Point Arithmetic Library for High-Accuracy Semidefinite Programming, 2017 IEEE 24th Symposium on Computer Arithmetic (ARITH), 2017.
DOI : 10.1109/ARITH.2017.18
URL : https://hal.archives-ouvertes.fr/hal-01491255
, Global Optimization with Polynomials and the Problem of Moments, SIAM Journal on Optimization, vol.11, issue.3, pp.796-817, 2001.
DOI : 10.1137/S1052623400366802
, Solving rank-constrained semidefinite programs in exact arithmetic, pp.357-364, 2016.
DOI : 10.1016/j.jsc.2017.07.009
URL : https://hal.archives-ouvertes.fr/hal-01363339
, Interior-point polynomial algorithms in convex programming, Studies in Applied Mathematics, vol.13, 1994.
DOI : 10.1137/1.9781611970791
, The algebraic degree of semidefinite programming, Mathematical Programming, pp.379-405, 2010.
DOI : 10.1007/978-1-4615-4381-7
, Semidefinite programming relaxations for semialgebraic problems, Mathematical Programming, vol.96, issue.2, pp.293-320, 2003.
DOI : 10.1007/s10107-003-0387-5
URL : http://control.ee.ethz.ch/~parrilo/pubs/files/SDPrelaxations.ps.gz
, An exact duality theory for semidefinite programming and its complexity implications, Mathematical Programming, pp.129-162, 1997.
DOI : 10.1515/9781400873173
, Safey El Din, Finding at least one point in each connected component of a real algebraic set defined by a single equation, J. Complexity, pp.16-716, 2000.
, Testing Sign Conditions on a Multivariate Polynomial and Applications, Mathematics in Computer Science, vol.1, issue.1, pp.177-207, 2007.
DOI : 10.1007/s11786-007-0003-9
URL : https://hal.archives-ouvertes.fr/inria-00105835
, Polar varieties and computation of one point in each connected component of a smooth real algebraic set, Proceedings of the 2003 international symposium on Symbolic and algebraic computation , ISSAC '03, pp.224-231, 2003.
DOI : 10.1145/860854.860901
URL : https://hal.archives-ouvertes.fr/inria-00099649
, A nearly optimal algorithm for deciding connectivity queries in smooth and bounded real algebraic sets, Journal of the ACM, vol.63, 2017.
URL : https://hal.archives-ouvertes.fr/hal-00849057
, Bit complexity for multi-homogeneous polynomial system solving -application to polynomial minimization, Journal of Symbolic Computation, vol.87, pp.176-206, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01319729
, Computing Rational Points in Convex Semialgebraic Sets and Sum of Squares Decompositions, SIAM Journal on Optimization, vol.20, issue.6, pp.2876-2889, 2010.
DOI : 10.1137/090772459
URL : https://hal.archives-ouvertes.fr/inria-00419983
, Sums of squares of polynomials with rational coefficients, Journal of the European Mathematical Society, vol.18, issue.7, pp.1495-1513, 2016.
DOI : 10.4171/JEMS/620
, Computing parametric geometric resolutions, Applicable Algebra in Engineering, Communication and Computing, vol.13, pp.349-393, 2003.
DOI : 10.1007/s00200-002-0109-x
URL : http://www.gage.polytechnique.fr/~schost/publications/parametr.ps
, Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones, Optimization Methods and Software, vol.81, issue.1-4, pp.625-653, 1999.
DOI : 10.1287/moor.19.1.53
URL : http://www.unimaas.nl/~sturm/papers/guide.ps.gz
, Sdpt3 ? a matlab software package for semidefinite programming, version 1.3, Optimization methods and software, pp.545-581, 1999.
DOI : 10.1080/10556789908805762