Real Algebraic Geometry, 1998. ,
DOI : 10.1007/978-3-662-03718-8
Determinantal rings, Lecture Notes in Math, vol.1327, 1988. ,
Ideals, Varieties, and Algorithms : An Introduction to Computational Algebraic Geometry and Commutative Algebra, 2005. ,
Solution of the truncated complex moment problem for flat data. Memoirs of the, pp.1-62, 1996. ,
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
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
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
Global optimization of polynomials using the truncated tangency variety, SIAM Journal on Optimization, vol.19, issue.2, pp.941-951, 2008. ,
Representation of positive polynomials and optimization on noncompact semialgebraic sets, SIAM Journal on Optimization, vol.20, issue.6, pp.3082-3103, 2010. ,
Positive Polynomials in Control, chapter Detecting Global Optimality and Extracting Solutions in GloptiPoly, Lectures Notes in Control and Information Sciences, pp.293-310, 2005. ,
Extremum problems with inequalities as side conditions, Studies and Essays, Courant Anniversary Volume, pp.187-204, 1948. ,
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
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
Moments, positive polynomials and their applications, p.210 ,
DOI : 10.1142/p665
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
A unified approach for real and complex zeros of zerodimensional ideals, Emerging Applications of Algebraic Geometry, pp.125-156, 2009. ,
Semidefinite representations for finite varieties, Mathematical Programming, vol.5, issue.1, pp.1-26, 2007. ,
DOI : 10.1007/s10107-004-0561-4
Sums of Squares, Moment Matrices and Optimization Over Polynomials, Mathematics and its Applications, pp.157-270, 2009. ,
DOI : 10.1007/978-0-387-09686-5_7
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
A certificate for semidefinite relaxations in computing positive dimensional real varieties, 2013. ,
The Fritz John necessary optimality conditions in the presence of equality and inequality constraints, Journal of Mathematical Analysis and Applications, vol.17, issue.1, pp.37-47, 1967. ,
DOI : 10.1016/0022-247X(67)90163-1
Optimization of Polynomial Functions, Bulletin canadien de math??matiques, vol.46, issue.4, pp.575-587, 2003. ,
DOI : 10.4153/CMB-2003-054-7
Representations of non-negative polynomials, degree bounds and applications to optimization . Can, J. Math, vol.61, issue.1, pp.205-221, 2009. ,
Squared Functional Systems and Optimization Problems, High performance optimization, pp.405-440, 2000. ,
DOI : 10.1007/978-1-4757-3216-0_17
An exact Jacobian SDP relaxation for polynomial optimization, Mathematical Programming, pp.1-31, 2011. ,
DOI : 10.1007/s10107-011-0489-4
Certifying convergence of Lasserre???s hierarchy via flat truncation, Mathematical Programming, pp.1-26, 2012. ,
DOI : 10.1007/s10107-012-0589-9
Polynomial Optimization with Real Varieties, SIAM Journal on Optimization, vol.23, issue.3, pp.1634-1646, 2013. ,
DOI : 10.1137/120898772
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
Semidefinite programming relaxations for semialgebraic problems, Mathematical Programming, vol.96, issue.2, pp.293-320, 2003. ,
DOI : 10.1007/s10107-003-0387-5
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. ,
Algebraic moments,real root finding and related topics, 2009. ,
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
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, 1974. ,