C. Aholt, S. Agarwal, and R. Thomas, A QCQP Approach to Triangulation, Computer Vision?ECCV 2012, pp.654-667, 2012.
DOI : 10.1007/978-3-642-33718-5_47

C. Aholt, B. Sturmfels, and R. Thomas, A hilbert scheme in computer vision, arXiv preprint, 2011.

B. Balasundaram and S. Butenko, Constructing test functions for global optimization using continuous formulations of graph problems, Optimization Methods and Software, vol.3, issue.4-5, pp.439-452, 2005.
DOI : 10.1023/A:1017969603632

B. Bank, M. Giusti, J. Heintz, and G. Mbakop, Polar Varieties, Real Equation Solving, and Data Structures: The Hypersurface Case, Polar varieties and efficient real elimination, pp.5-27, 1997.
DOI : 10.1006/jcom.1997.0432

B. Bank, M. Giusti, J. Heintz, and M. , 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

B. Bank, M. Giusti, J. Heintz, and M. , Safey El Din, and E. Schost, On the geometry of polar varieties, Applicable Algebra in Engineering, 2010.

S. Basu, R. Pollack, and M. Roy, On the combinatorial and algebraic complexity of quantifier elimination, Algorithms in real algebraic geometry, pp.1002-1045, 1996.
DOI : 10.1145/235809.235813

W. Baur and V. Strassen, The complexity of partial derivatives, Theoretical Computer Science, vol.22, issue.3, pp.317-330, 1983.
DOI : 10.1016/0304-3975(83)90110-X

C. W. Brown, Solution formula construction for truth-invariant cads, 1999.

T. F. Coleman and A. P. Liao, An efficient trust region method for unconstrained discrete-time optimal control problems, Computational Optimization and Applications, vol.15, issue.1, pp.47-66, 1995.
DOI : 10.1007/BF01299158

G. E. Collins, Quantifier elimination for real closed fields by cylindrical algebraic decomposition, Automata theory and formal languages (Second GI Conf. Automata theory and formal languages (Second GI Conf, pp.134-183, 1975.

G. E. Collins and H. Hong, Partial cylindrical algebraic decomposition for quantifier elimination , in Quantifier elimination and cylindrical algebraic decomposition (Linz, 1993), Texts Monogr, Symbol. Comput, pp.174-200, 1998.

P. Cousot, Proving Program Invariance and Termination by Parametric Abstraction, Lagrangian Relaxation and Semidefinite Programming, Lecture Notes in Computer Science, vol.3385, pp.1-24, 2005.
DOI : 10.1007/978-3-540-30579-8_1

J. Demmel, J. Nie, and V. Powers, 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

M. M. Deza and M. Laurent, Geometry of cuts and metrics, Algorithms and Combinatorics, vol.15, 2010.
DOI : 10.1007/978-3-642-04295-9

D. Eisenbud, Commutative algebra with a view toward algebraic geometry, 1995.

H. Everett, D. Lazard, S. Lazard, and M. , The Voronoi Diagram of Three Lines, Discrete & Computational Geometry, vol.1, issue.4, pp.94-130, 2009.
DOI : 10.1007/s00454-009-9173-3

URL : https://hal.archives-ouvertes.fr/inria-00186085

J. Faugère, A new efficient algorithm for computing Gr??bner bases (F4), Journal of Pure and Applied Algebra, vol.139, issue.1-3, pp.61-88, 1998.
DOI : 10.1016/S0022-4049(99)00005-5

J. Faugère, P. Gaudry, L. Huot, and G. Renault, Polynomial systems solving by fast linear algebra, 2013.

J. Faugère, P. Gianni, D. Lazard, and T. Mora, Efficient Computation of Zero-dimensional Gr??bner Bases by Change of Ordering, Journal of Symbolic Computation, vol.16, issue.4, pp.329-344, 1993.
DOI : 10.1006/jsco.1993.1051

J. Faugère and C. Mou, Fast algorithm for change of ordering of zero-dimensional gröbner bases with sparse multiplication matrices, Proceedings of the 36th international symposium on Symbolic and algebraic computation, pp.115-122, 2011.

J. Faugère, M. Safey-el-din, and P. Spaenlehauer, Critical points and gröbner bases: the unmixed case, Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, pp.2012-162

P. Festa, P. M. Pardalos, M. G. Resende, and C. C. Ribeiro, Randomized heuristics for the Max-Cut problem, Optimization Methods and Software, vol.25, issue.6, pp.1033-1058, 2002.
DOI : 10.1080/1055678021000090033

M. Giusti, G. Lecerf, and B. Salvy, 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

A. Greuet and M. S. Din, Deciding reachability of the infimum of a multivariate polynomial, Proceedings of the 36th international symposium on Symbolic and algebraic computation, ISSAC '11, pp.131-138, 2011.
DOI : 10.1145/1993886.1993910

URL : https://hal.archives-ouvertes.fr/hal-00744469

A. Greuet, F. Guo, M. S. Din, and L. Zhi, Global optimization of polynomials restricted to a smooth variety using sums of squares, Journal of Symbolic Computation, vol.47, issue.5, pp.47-503, 2012.
DOI : 10.1016/j.jsc.2011.12.003

URL : https://hal.archives-ouvertes.fr/hal-00744605

F. Guo and M. , Safey El Din, and L. Zhi, Global optimization of polynomials using generalized critical values and sums of squares, Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, 2010.

Q. Guo, M. Safey-el-din, and L. Zhi, 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

J. Heintz and C. Schnorr, Testing polynomials which are easy to compute (extended abstract), in STOC, pp.262-272, 1980.

D. Henrion and J. Lasserre, GloptiPoly, ACM Transactions on Mathematical Software, vol.29, issue.2, pp.29-165, 2003.
DOI : 10.1145/779359.779363

URL : https://hal.archives-ouvertes.fr/hal-00172442

D. Henrion, M. Sebek, and V. Ku?era, Positive polynomials and robust stabilization with fixed-order controllers, IEEE Transactions on Automatic Control, vol.48, issue.7, pp.48-1178, 2003.
DOI : 10.1109/TAC.2003.814103

H. Hong, Simple solution formula construction in cylindrical algebraic decomposition based quantifier elimination, Papers from the international symposium on Symbolic and algebraic computation, ISSAC '92, pp.177-188, 1992.

H. Hong and M. , Safey El Din, Variant real quantifier elimination: algorithm and application, Proceedings of the 2009 international symposium on Symbolic and algebraic computation, pp.183-190, 2009.

Z. Jelonek, Testing sets for properness of polynomial mappings, Mathematische Annalen, vol.315, issue.1, pp.1-35, 1999.
DOI : 10.1007/s002080050316

E. Kaltofen, On computing determinants of matrices without divisions, Papers from the international symposium on Symbolic and algebraic computation , ISSAC '92, pp.342-349, 1992.
DOI : 10.1145/143242.143350

E. L. Kaltofen, B. Li, Z. Yang, and L. Zhi, Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients, Journal of Symbolic Computation, vol.47, issue.1, pp.47-48, 2012.
DOI : 10.1016/j.jsc.2011.08.002

T. Krick, L. M. Pardo, and M. Sombra, Sharp estimates for the arithmetic nullstellensatz, Duke Mathematical Journal, vol.109, pp.521-598, 2001.

E. Kunz, Introduction to commutative algebra and algebraic geometry, 1984.
DOI : 10.1007/978-1-4612-5290-0

J. Lasserre, 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

A. Lax and P. D. Lax, On sums of squares, Linear Algebra and Appl, pp.71-75, 1978.

D. Lazard and F. Rouillier, Solving parametric polynomial systems, Journal of Symbolic Computation, vol.42, issue.6, pp.636-667, 2007.
DOI : 10.1016/j.jsc.2007.01.007

URL : https://hal.archives-ouvertes.fr/hal-01148721

G. Lecerf, Computing the equidimensional decomposition of an algebraic closed set by means of lifting fibers, Journal of Complexity, vol.19, issue.4, pp.564-596, 2003.
DOI : 10.1016/S0885-064X(03)00031-1

URL : https://hal.archives-ouvertes.fr/hal-00186727

J. Löfberg, 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

A. Logar, A computational proof of the noether normalization lemma, in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, pp.259-273, 1989.

S. Mccallum, An improved projection operation for cylindrical algebraic decomposition, in Quantifier elimination and cylindrical algebraic decomposition (Linz, 1993), Texts Monogr, Symbol. Comput, pp.242-268, 1998.

D. Monniaux, On using sums-of-squares for exact computations without strict feasibility, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00487279

Y. Nesterov, Squared functional systems and optimization problems, High performance optimization, pp.405-440, 2000.

J. Nie, An exact Jacobian SDP relaxation for polynomial optimization, Mathematical Programming, vol.207, issue.3, 2011.
DOI : 10.1007/s10107-011-0489-4

J. Nie, J. Demmel, and B. Sturmfels, 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

P. A. Parrilo, Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization, dissertation (Ph, California Institute of Technology, 2000.

H. Peyrl and P. A. Parrilo, Computing sum of squares decompositions with rational coefficients, Symbolic-Numerical Computations, pp.269-281, 2008.
DOI : 10.1016/j.tcs.2008.09.025

S. Prajna, A. Papachristodoulou, P. Seiler, and P. Parrilo, Sostools: Sum of squares optimization toolbox for matlab, 2004.

F. Rouillier, Solving Zero-Dimensional Systems Through the Rational Univariate Representation, Applicable Algebra in Engineering, Communication and Computing, vol.9, issue.5, pp.433-461, 1999.
DOI : 10.1007/s002000050114

URL : https://hal.archives-ouvertes.fr/inria-00073264

F. Rouillier, M. Roy, and M. , 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.

F. Rouillier and P. Zimmermann, Efficient isolation of polynomial's real roots, Proceedings of the International Conference on Linear Algebra and Arithmetic, pp.33-50, 2001.
DOI : 10.1016/j.cam.2003.08.015

M. Safey-el-din, 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

M. Safey-el-din, Computing the global optimum of a multivariate polynomial over the reals, ISSAC, pp.71-78, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01305635

M. Schost, Polar varieties and computation of one point in each connected component of a smooth algebraic set Properness defects of projections and computation of at least one point in each connected component of a real algebraic set, Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation, pp.224-231, 2003.

M. Safey-el-din and E. Schost, A nearly optimal algorithm for deciding connectivity queries in smooth and bounded real algebraic sets, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00849057

M. Safey-el-din and L. Zhi, Computing Rational Points in Convex Semialgebraic Sets and Sum of Squares Decompositions, Schost, Computing parametric geometric resolutions, Applicable Algebra in Engineering, Communication and Computing, pp.2876-2889, 2003.
DOI : 10.1137/090772459

URL : https://hal.archives-ouvertes.fr/inria-00419983

M. Schweighofer, 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

I. Shafarevich, Basic Algebraic Geometry 1, 1977.

N. Z. Shor, An approach to obtaining global extrema in polynomial problems of mathematical programming, Kibernetika (Kiev), vol.136, pp.102-106, 1987.

P. Spaenlehauer, Complexity bounds for computing critical points with gr\ " obner bases algorithms: the mixed case, 2013.