L. Blum, F. Cucker, M. Shub, and S. Smale, Complexity and real computation, 2012.
DOI : 10.1007/978-1-4612-0701-6

B. Bank, M. Giusti, J. Heintz, and L. Pardo, Generalized polar varieties: geometry and algorithms, Journal of complexity, vol.21, issue.4, p.377412, 2005.
DOI : 10.1016/j.jco.2004.10.001
URL : https://doi.org/10.1016/j.jco.2004.10.001

S. Boyd, S. Kim, L. Vandenberghe, and A. Hassibi, A tutorial on geometric programming, Optim. Eng, vol.8, issue.1, p.67127, 2007.
DOI : 10.1007/s11081-007-9001-7

S. Basu, R. Pollack, and M. Roy, A new algorithm to nd a point in every cell dened by a family of polynomials. In Quantier elimination and cylindrical algebraic decomposition, 1998.

S. Boyd and L. Vandenberghe, Convex optimization, 2004.

S. Chevillard, J. Harrison, M. Joldes, and C. Lauter, Ecient and accurate computation of upper bounds of approximation errors, Theoretical Computer Science, vol.412, issue.16, pp.1523-1543, 2011.

G. E. Collins, Quantier elimination for real closed elds by cylindrical algebraic decompostion, ATFL 2nd GI Conf. Kaiserslautern, p.134183, 1975.
DOI : 10.1007/3-540-07407-4_17
URL : https://link.springer.com/content/pdf/10.1007%2F3-540-07407-4_17.pdf

V. Chandrasekaran and P. Shah, Relative Entropy Relaxations for Signomial Optimization
DOI : 10.1137/140988978
URL : http://arxiv.org/pdf/1409.7640

, SIAM J. Optim, vol.26, issue.2, p.11471173, 2016.

S. Diamond and S. Boyd, CVXPY: A Python-embedded modeling language for convex optimization, Journal of Machine Learning Research, 2016.

A. Domahidi, E. Chu, and S. Boyd, ECOS: An SOCP solver for embedded systems, European Control Conference (ECC), p.30713076, 2013.

M. Dressler, S. Iliman, and T. De-wol, An approach to constrained polynomial optimization via nonnegative circuit polynomials and geometric programming, Journal of Symbolic Computation, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01829714

M. Dressler, S. Iliman, and T. De-wol, A Positivstellensatz for Sums of Nonnegative Circuit Polynomials, SIAM J. Appl. Algebra Geom, vol.1, issue.1, p.536555, 2017.

R. Dun, E. Peterson, and C. Zener, Geometric programming: Theory and application, 1967.

T. De-wol, Amoebas, nonnegative polynomials and sums of squares supported on circuits, Oberwolfach Rep, issue.23, p.13081311, 2015.

G. H. Golub and C. F. Loan, Matrix Computations, 1996.

M. Ghasemi and M. Marshall, Lower bounds for polynomials using geometric programming

, SIAM J. Optim, vol.22, issue.2, p.460473, 2012.

M. Ghasemi and M. Marshall, Lower bounds for a polynomial on a basic closed semialgebraic set using geometric programming, 2013.

D. Grigoriev and N. Vorobjov, Solving systems of polynomials inequalities in subexponential time, Journal of Symbolic Computation, vol.5, p.3764, 1988.

]. T. Hab-+-17, M. Hales, G. Adams, D. T. Bauer, J. Dat et al., A Formal Proof of the Kepler Conjecture. Forum of Mathematics, 2017.

S. Iliman and T. De-wol, Amoebas, nonnegative polynomials and sums of squares supported on circuits, Res. Math. Sci, vol.3, pp.3-9, 2016.

D. Joyner, O. ƒertík, A. Meurer, and B. E. Granger, Open source computer algebra systems, Sympy. ACM Commun. Comput. Algebra, vol.45, p.225234, 2012.

J. Lasserre, Global optimization with polynomials and the problem of moments, SIAM Journal on Optimization, vol.11, issue.3, p.796817, 2001.

J. Lasserre, Convergent SDP-Relaxations in Polynomial Optimization with Sparsity, SIAM Journal on Optimization, vol.17, issue.3, p.822843, 2006.

J. Lasserre, Moments, positive polynomials and their applications, vol.1, 2010.

M. Laurent, Sums of squares, moment matrices and optimization over polynomials, Emerging applications of algebraic geometry, vol.149, p.157270

J. Lasserre, K. Toh, and S. Yang, A bounded degree SOS hierarchy for polynomial optimization, EURO Journal on Computational Optimization, vol.5, issue.1-2, p.87117, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01109125

V. Magron, X. Allamigeon, S. Gaubert, and B. Werner, Formal proofs for Nonlinear Optimization, Journal of Formalized Reasoning, vol.8, issue.1, p.124, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00985675

V. Magron, G. Constantinides, and A. Donaldson, Certied Roundo Error Bounds Using Semidenite Programming, ACM Trans. Math. Softw, vol.43, issue.4, p.134, 2017.

R. Murray, V. Chandrasekaran, and A. Wierman, Newton polytopes and relative entropy optimization, 2018.

V. Magron and M. S. Din, On Exact Polya and Putinar's Representations, ISSAC'18: Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation, 2018.

V. Magron and M. S. Din, RealCertify: a Maple package for certifying non-negativity, ISSAC'18: Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01956812

V. Magron, M. S. Din, and M. Schweighofer, Algorithms for weighted sum of squares decomposition of non-negative univariate polynomials, Journal of Symbolic Computation, 2018.

M. Mignotte, Mathematics for Computer Algebra, 1992.

V. Magron and M. , Safey El Din. On Exact Polya, 2018.

J. Oxley, Matroid theory, Oxford Graduate Texts in Mathematics, vol.21, 2011.

P. A. Parrilo, Structured Semidenite Programs and Semialgebraic Geometry Methods in Robustness and Optimization, California Inst. Tech, 2000.

H. Peyrl and P. Parrilo, Computing sum of squares decompositions with rational coecients, Theoretical Computer Science, vol.409, issue.2, p.269281, 2008.

J. Renegar, A faster PSPACE algorithm for deciding the existential theory of the reals, Foundations of Computer Science, p.291295, 1988.

J. Renegar, A Mathematical View of Interior-Point Methods in Convex Optimization, SIAM, 2001.

C. Riener, T. Theobald, L. J. Andrén, and J. Lasserre, Exploiting Symmetries in SDPRelaxations for Polynomial Optimization, Mathematics of Operations Research, vol.38, pp.122-141, 2013.

H. Seidler and T. De-wol, An experimental comparison of sonc and sos certicates for unconstrained optimization, 2018.

H. Seidler and T. De-wol, POEM: Eective methods in polynomial optimization, 2018.

H. Waki, S. Kim, M. Kojima, and M. Muramatsu, Sums of Squares and Semidenite Programming Relaxations for Polynomial Optimization Problems with Structured Sparsity, SIAM Journal on Optimization, vol.17, issue.1, p.218242, 2006.

T. Weisser, J. Lasserre, and K. Toh, Sparse-BSOS: a bounded degree SOS hierarchy for large scale polynomial optimization with sparsity, Mathematical Programming Computation, vol.10, issue.1, p.132, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01341931