Introduction to commutative algebra, 1969. ,
Polar Varieties, Real Equation Solving, and Data Structures: The Hypersurface Case, Journal of Complexity, vol.13, issue.1, pp.5-27, 1997. ,
DOI : 10.1006/jcom.1997.0432
Generalized polar varieties: geometry and algorithms, Journal of Complexity, vol.21, issue.4, pp.377-412, 2005. ,
DOI : 10.1016/j.jco.2004.10.001
On the geometry of polar varieties, Applicable Algebra in Engineering, Communication and Computing, vol.43, issue.2, pp.33-83, 2010. ,
DOI : 10.1007/s00200-009-0117-1
URL : https://hal.archives-ouvertes.fr/hal-01148162
Algorithms in real algebraic geometry, 2006. ,
DOI : 10.1007/978-3-662-05355-3
URL : https://hal.archives-ouvertes.fr/hal-01083587
There are significantly more nonegative polynomials than sums of squares, Israel Journal of Mathematics, vol.253, issue.2, pp.355-380, 2006. ,
DOI : 10.1007/BF02771790
Real algebraic geometry, 1998. ,
DOI : 10.1007/978-3-662-03718-8
Convex Optimization, 2004. ,
The Number of Equations Defining a Determinantal Variety, Bulletin of the London Mathematical Society, vol.22, issue.5, pp.439-445, 1990. ,
DOI : 10.1112/blms/22.5.439
Proving Program Invariance and Termination by Parametric Abstraction, Lagrangian Relaxation and Semidefinite Programming, Verification, Model Checking, and Abstract Interpretation, pp.1-24, 2005. ,
DOI : 10.1007/978-3-540-30579-8_1
Representations of positive polynomials on noncompact semialgebraic sets via KKT ideals, Journal of Pure and Applied Algebra, vol.209, issue.1, pp.189-200, 2007. ,
DOI : 10.1016/j.jpaa.2006.05.028
Commutative algebra with a view toward algebraic geometry, 1995. ,
Global optimization of polynomials using generalized critical values and sums of squares, Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC '10, pp.107-114, 2010. ,
DOI : 10.1145/1837934.1837960
URL : https://hal.archives-ouvertes.fr/hal-01292624
Solving polynomial optimization problems via the truncated tangency variety and sums of squares, J. Pure Appl. Algebra, vol.213, issue.11, pp.2167-2176, 2009. ,
GloptiPoly, ACM Transactions on Mathematical Software, vol.29, issue.2, pp.165-194, 2003. ,
DOI : 10.1145/779359.779363
URL : https://hal.archives-ouvertes.fr/hal-00172442
Positive polynomials and robust stabilization with fixed-order controllers, IEEE Transactions on Automatic Control, vol.48, issue.7, pp.1178-1186, 2003. ,
DOI : 10.1109/TAC.2003.814103
Ueber die Darstellung definiter Formen als Summe von Formenquadraten, Mathematische Annalen, vol.32, issue.3, pp.342-350, 1888. ,
DOI : 10.1007/BF01443605
Testing sets for properness of polynomial mappings, Mathematische Annalen, vol.315, issue.1, pp.1-35, 1999. ,
DOI : 10.1007/s002080050316
Introduction to commutative algebra and algebraic geometry, 1988. ,
DOI : 10.1007/978-1-4612-5290-0
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
Introduction to Smooth Manifolds, 2002. ,
YALMIP : a toolbox for modeling and optimization in MATLAB, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508), 2004. ,
DOI : 10.1109/CACSD.2004.1393890
On using sums-of-squares for exact computations without strict feasibility, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00487279
Algebraic Geometry I, Complex projective varieties, Classics in Mathematics, 1976. ,
DOI : 10.1007/978-3-642-61833-8
An exact jacobian SDP relaxation for polynomial optimization, preprint. URL http://math, 2010. ,
Minimizing Polynomials via Sum of Squares over the Gradient Ideal, Mathematical Programming, vol.13, issue.3, pp.587-606, 2006. ,
DOI : 10.1007/s10107-005-0672-6
Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. Dissertation (Ph, California Institute of Tech- nology, 2000. ,
Minimizing polynomial functions In: Algorithmic and quantitative real algebraic geometry, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. Amer. Math. Soc, vol.60, pp.83-99, 2001. ,
SOSTOOLS: Sum of squares optimization toolbox for MATLAB. URL http Polar varieties and computation of one point in each connected component of a smooth algebraic set, Proceedings of the, 2003. ,
A Baby Steps/Giant Steps Probabilistic Algorithm for??Computing Roadmaps in Smooth Bounded Real Hypersurface, Discrete & Computational Geometry, vol.43, issue.3, pp.181-220, 2011. ,
DOI : 10.1007/s00454-009-9239-2
Global Optimization of Polynomials Using Gradient Tentacles and Sums of Squares, SIAM Journal on Optimization, vol.17, issue.3, pp.920-942, 2006. ,
DOI : 10.1137/050647098
Basic Algebraic Geometry 1, 1977. ,
An approach to obtaining global extrema in polynomial problems of mathematical programming, Kibernetika (Kiev), vol.136, issue.5, pp.102-106, 1987. ,
Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw, pp.1-4, 1999. ,
Algorithm 883, ACM Transactions on Mathematical Software, vol.35, issue.2, pp.1-1513, 2009. ,
DOI : 10.1145/1377612.1377619
Commutative algebra, 1958. ,
DOI : 10.1007/978-3-662-29244-0