J. Bochnak, M. Coste, and M. Roy, Real Algebraic Geometry, 1998.
DOI : 10.1007/978-3-662-03718-8

S. Boyd and L. Vandenbergh, Convex Optimization, 2004.

D. A. Cox, J. B. Little, and D. B. Shea, Using Algebraic Geometry, 1998.
DOI : 10.1007/978-1-4757-6911-1

D. A. Cox, J. B. Little, and D. B. Shea, Ideals, Varieties, and Algorithms : An Introduction to Computational Algebraic Geometry and Commutative Algebra, 2005.

R. E. Curto and L. Fialkow, Solution of the truncated complex moment problem for flat data. Memoirs of the, pp.1-62, 1996.

M. Elkadi and B. Mourrain, Introduction à la résolution des systèmes d'équations algébriques, of Mathématiques et Applications, 2007.

S. Graillat, . Ph, and . Trébuchet, A new algorithm for computing certified numerical approximations of the roots of a zero-dimensional system, Proceedings of the 2009 international symposium on Symbolic and algebraic computation, ISSAC '09, pp.167-173, 2009.
DOI : 10.1145/1576702.1576727
URL : https://hal.archives-ouvertes.fr/hal-01294713

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

F. Guo, 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, ISSAC '10, pp.107-114, 2010.
DOI : 10.1145/1837934.1837960
URL : https://hal.archives-ouvertes.fr/hal-01292624

B. Hanzon and D. Jibetean, Global minimization of a multivariate polynomial using matrix methods, Journal of Global Optimization, vol.27, issue.1, pp.1-23, 2001.
DOI : 10.1023/A:1024664432540

D. Jibetean and M. Laurent, Semidefinite Approximations for Global Unconstrained Polynomial Optimization, SIAM Journal on Optimization, vol.16, issue.2, pp.490-514, 2005.
DOI : 10.1137/04060562X

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.1-15, 2012.
DOI : 10.1016/j.jsc.2011.08.002

J. Lasserre, M. Laurent, B. Mourrain, P. Rostalski, and P. Trébuchet, Moment matrices, border bases and real radical computation, Journal of Symbolic Computation, vol.51, 2012.
DOI : 10.1016/j.jsc.2012.03.007
URL : https://hal.archives-ouvertes.fr/hal-00651759

J. B. 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

J. B. Lasserre, M. Laurent, and P. Rostalski, Semidefinite Characterization and Computation of Zero-Dimensional Real Radical Ideals, Foundations of Computational Mathematics, vol.16, issue.1, pp.607-647, 2008.
DOI : 10.1007/s10208-007-9004-y

J. B. Lasserre, M. Laurent, and P. Rostalski, A unified approach for real and complex zeros of zerodimensional ideals, Emerging Applications of Algebraic Geometry, pp.125-156, 2009.

M. Laurent, Semidefinite representations for finite varieties, Mathematical Programming, vol.5, issue.1, pp.1-26, 2007.
DOI : 10.1007/s10107-004-0561-4

M. Laurent and B. Mourrain, A generalized flat extension theorem for moment matrices, Archiv der Mathematik, vol.38, issue.1, pp.87-98, 2009.
DOI : 10.1007/s00013-009-0007-6

M. Marshall, Optimization of Polynomial Functions, Bulletin canadien de math??matiques, vol.46, issue.4, pp.575-587, 2003.
DOI : 10.4153/CMB-2003-054-7

B. Mourrain, A New Criterion for Normal Form Algorithms, Proc. AAECC, pp.430-443, 1999.
DOI : 10.1007/3-540-46796-3_41

B. Mourrain and P. Trébuchet, Generalized normal forms and polynomial system solving, Proceedings of the 2005 international symposium on Symbolic and algebraic computation , ISSAC '05, pp.253-260, 2005.
DOI : 10.1145/1073884.1073920
URL : https://hal.archives-ouvertes.fr/inria-00070537

B. Mourrain, . Ph, and . Trébuchet, Stable normal forms for polynomial system solving, Theoretical Computer Science, vol.409, issue.2, pp.229-240, 2008.
DOI : 10.1016/j.tcs.2008.09.004
URL : https://hal.archives-ouvertes.fr/inria-00343103

Y. Nesterov, Squared Functional Systems and Optimization Problems, High performance optimization, pp.405-440, 2000.
DOI : 10.1007/978-1-4757-3216-0_17

J. Nie, An exact Jacobian SDP relaxation for polynomial optimization, Mathematical Programming, pp.1-31, 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, Semidefinite programming relaxations for semialgebraic problems, Mathematical Programming, vol.96, issue.2, pp.293-320, 2003.
DOI : 10.1007/s10107-003-0387-5

P. A. Parrilo and B. Sturmfels, Minimizing polynomial functions, Proceedings of the DIMACS Workshop on Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science, pp.83-100, 2003.

W. Rudin, Functional analysis. International Series in Pure and Applied Mathematics, 1991.

M. Safey-el-din, Computing the global optimum of a multivariate polynomial over the reals, Proceedings of the twenty-first international symposium on Symbolic and algebraic computation, ISSAC '08, pp.71-78, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01305635

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

N. Z. Shor, Class of global minimum bounds of polynomial functions, Cybernetics, vol.5, issue.No. 3, pp.731-734, 1987.
DOI : 10.1007/BF01070233

. Ph, B. Trébuchet, and . Mourrain, Border basis representation of a general quotient algebra, pp.265-272, 2012.