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

URL : http://doi.org/10.1016/j.jco.2004.10.001

B. Bank, M. Giusti, J. Heintz, and M. , Intrinsic complexity estimates in polynomial optimization, Journal of Complexity, vol.30, issue.4, pp.430-443, 2014.
DOI : 10.1016/j.jco.2014.02.005

URL : https://hal.archives-ouvertes.fr/hal-00815123

B. Bank, M. Giusti, J. Heintz, M. Safey-el-din, and E. Schost, 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

E. Becker, T. Mora, M. G. Marinari, and C. Traverso, The shape of the Shape Lemma, Proceedings of the international symposium on Symbolic and algebraic computation , ISSAC '94, pp.129-133, 1994.
DOI : 10.1145/190347.190382

D. P. Garcia and M. Morari, Model predictive control: Theory and practice???A survey, Automatica, vol.25, issue.3, pp.335-348, 1989.
DOI : 10.1016/0005-1098(89)90002-2

F. Catanese, S. Hosten, A. Khetan, and B. Sturmfels, The maximum likelihood degree, American Journal of Mathematics, vol.128, issue.3, pp.671-677, 2006.
DOI : 10.1353/ajm.2006.0019

C. Chen, O. Golubitsky, F. Lemaire, M. M. Maza, and W. Pan, Comprehensive Triangular Decomposition, Computer Algebra in Scientific Computing, 10th International Workshop Proceedings, pp.73-101, 2007.
DOI : 10.1007/978-3-540-75187-8_7

G. Collins, Quantifier elimination for real closed fields by cylindrical algebraic decompostion, Lecture Notes in Computer Science, vol.33, pp.134-183, 1975.
DOI : 10.1007/3-540-07407-4_17

D. Cox, J. Little, and D. Shea, Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, Undergraduate Texts in Mathematics, 2007.

J. , D. Dora, C. Discrescenzo, and D. Duval, About a new method method for computing in algebraic number fields, In EUROCAL LNCS, vol.85, issue.204, pp.289-290, 1985.

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. V. Gathen and J. Gerhard, Modern computer algebra, 1999.

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

H. Graf-von-bothmer and K. Ranestad, A general formula for the algebraic degree in semidefinite programming, Bulletin of the London Mathematical Society, vol.41, issue.2, pp.193-197, 2009.
DOI : 10.1112/blms/bdn114

A. Greuet, F. Guo, M. Safey-el-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.503-518, 2012.
DOI : 10.1016/j.jsc.2011.12.003

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

A. Greuet and M. Safey-el-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 and M. Safey-el-din, Probabilistic Algorithm for Polynomial Optimization over a Real Algebraic Set, SIAM Journal on Optimization, vol.24, issue.3, pp.1313-1343, 2014.
DOI : 10.1137/130931308

URL : https://hal.archives-ouvertes.fr/hal-00849523

F. Guo, C. Wang, and L. Zhi, Optimizing a linear function over a noncompact real algebraic variety, Proceedings of the 2014 Symposium on Symbolic-Numeric Computation, SNC '14, pp.39-40, 2014.
DOI : 10.1145/2631948.2631957

URL : https://hal.archives-ouvertes.fr/hal-01237920

S. Hosten, A. Khetan, and B. Sturmfels, Solving the Likelihood Equations, Foundations of Computational Mathematics, vol.5, issue.4, pp.389-407, 2005.
DOI : 10.1007/s10208-004-0156-8

Z. Jelonek and K. Kurdyka, Quantitative Generalized Bertini-Sard Theorem for Smooth Affine Varieties, Discrete & Computational Geometry, vol.34, issue.4, pp.659-678, 2005.
DOI : 10.1007/s00454-005-1203-1

URL : https://hal.archives-ouvertes.fr/hal-00389073

K. Kurdyka, P. Orro, and S. Simon, Semialgebraic Sard Theorem for Generalized Critical Values, Journal of Differential Geometry, vol.56, issue.1, pp.67-92, 2000.
DOI : 10.4310/jdg/1090347525

X. Li, M. M. Maza, and W. Pan, Computations modulo regular chains, Proceedings of the 2009 international symposium on Symbolic and algebraic computation, ISSAC '09, pp.239-246, 2009.
DOI : 10.1145/1576702.1576736

J. Nie and K. Ranestad, Algebraic Degree of Polynomial Optimization, SIAM Journal on Optimization, vol.20, issue.1, pp.485-502, 2009.
DOI : 10.1137/080716670

J. Nie, K. Ranestad, and B. Sturmfels, The algebraic degree of semidefinite programming, Mathematical Programming, pp.379-405, 2010.
DOI : 10.1007/s10107-008-0253-6

P. J. Rabier, Ehresmann Fibrations and Palais-Smale Conditions for Morphisms of Finsler Manifolds, The Annals of Mathematics, vol.146, issue.3, pp.647-691, 1997.
DOI : 10.2307/2952457

K. Ranestad, Algebraic Degree in Semidefinite and Polynomial Optimization, Handbook on Semidefinite, Conic and Polynomial Optimization of International Series in Operations Research & Management Science, pp.61-75, 2012.
DOI : 10.1007/978-1-4614-0769-0_3

R. Rockafellar, Convex Analysis. Convex Analysis, 1970.

P. Rostalski and B. Sturmfels, Dualities in convex algebraic geometry, Rendiconti di Matematica, Serie VII, vol.30, pp.285-327, 2010.

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

M. Safey-el-din and E. Schost, 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

M. Safey-el-din and E. Schost, Properness defects of projections and computation of at least one point in each connected component of a real algebraic set, Discrete & Computational Geometry, vol.32, issue.3, pp.417-430, 2004.
URL : https://hal.archives-ouvertes.fr/inria-00099962

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

R. Sinn, Algebraic boundaries of convex semi-algebraic sets, Research in the Mathematical Sciences, vol.62, issue.4, 2014.
DOI : 10.1186/s40687-015-0022-0

H. Vui and P. S?-on, Representations of Positive Polynomials and Optimization on Noncompact Semialgebraic Sets, SIAM Journal on Optimization, vol.20, issue.6, pp.3082-3103, 2010.
DOI : 10.1137/090772903

V. Weispfenning, Comprehensive Gr??bner bases, Journal of Symbolic Computation, vol.14, issue.1, pp.1-29, 1992.
DOI : 10.1016/0747-7171(92)90023-W