Sum-of-Squares Proofs and the Quest toward Optimal Algorithms, Proc. ICM 2014 ,
New upper bounds for kissing numbers from semidefinite programming, Journal of the American Mathematical Society, vol.21, issue.3, pp.909-924, 2008. ,
DOI : 10.1090/S0894-0347-07-00589-9
URL : https://hal.archives-ouvertes.fr/hal-00196156
The Interplay Between Big Data and Sparsity in Systems Identification, Tracts in Advanced Robotics, vol.17, issue.3, pp.133-159, 2017. ,
DOI : 10.1137/05064504X
Towards a Mathematical Theory of Super-resolution, Communications on Pure and Applied Mathematics, vol.52, issue.3, pp.906-956, 2014. ,
DOI : 10.1007/b105056
Set-Membership Error-in-Variables Identification Through Convex Relaxation Techniques, IEEE Transactions on Automatic Control, vol.57, issue.2, pp.517-522, 2012. ,
DOI : 10.1109/TAC.2011.2168073
Exact Solutions to Super Resolution on Semi-Algebraic Domains in Higher Dimensions, IEEE Transactions on Information Theory, vol.63, issue.1, pp.621-630, 2017. ,
DOI : 10.1109/TIT.2016.2619368
URL : https://hal.archives-ouvertes.fr/hal-01114328
Approximate Optimal Designs for Multivariate Polynomial Regression, LAAS report No 17044, 2017. ,
Bound-Constrained Polynomial Optimization Using Only Elementary Calculations, Mathematics of Operations Research, vol.42, issue.3, pp.42-834, 2017. ,
DOI : 10.1287/moor.2016.0829
URL : https://hal.archives-ouvertes.fr/hal-01698348
A semidefinite programming hierarchy for packing problems in discrete geometry, Mathematical Programming, vol.74, issue.2, pp.1-25, 2015. ,
DOI : 10.1090/S0002-9904-1968-12104-4
Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming, Journal of the ACM, vol.42, issue.6, pp.1115-1145, 1995. ,
DOI : 10.1145/227683.227684
, Transactions of the American Mathematical Society, vol.356, issue.09, pp.3721-3737, 2004.
DOI : 10.1090/S0002-9947-04-03433-6
Convex Computation of the Region of Attraction of Polynomial Control Systems, IEEE Transactions on Automatic Control, vol.59, issue.2, pp.297-312, 2014. ,
DOI : 10.1109/TAC.2013.2283095
URL : https://hal.archives-ouvertes.fr/hal-00723019
Convergent Relaxations of Polynomial Matrix Inequalities and Static Output Feedback, IEEE Transactions on Automatic Control, vol.51, issue.2, pp.192-202, 2006. ,
DOI : 10.1109/TAC.2005.863494
GloptiPoly 3: moments, optimization and semidefinite programming, Optimization Methods and Software, vol.24, issue.4-5, pp.761-779, 2009. ,
DOI : 10.1080/10556780802699201
URL : https://hal.archives-ouvertes.fr/hal-00172442
Approximate Volume and Integration for Basic Semialgebraic Sets, SIAM Review, vol.51, issue.4, pp.722-743, 2009. ,
DOI : 10.1137/080730287
URL : https://hal.archives-ouvertes.fr/hal-00297384
Sparse polynomial interpolation: compressed sensing, super resolution, or Prony?, LAAS Report no 17279, 2017. ,
Innapproximability of NP-complete Problems, Discrete Fourier Analysis, and Geometry, Proc. ICM 2010, 2010. ,
Hardness of approximation, Proc. ICM 2014, 2014. ,
Anneaux pr??ordonn??s, Journal d'Analyse Math??matique, vol.12, issue.1, pp.307-326, 1964. ,
DOI : 10.1007/BF02807438
Quelques propriétés des préordres dans les anneaux commutatifs, C.R. Acd. Sci. Paris, Ser. I, vol.258, pp.3417-3418, 1964. ,
, Moments in Mathematics, Proc. Sympos, 1987.
Optimisation globale et th??orie des moments, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.331, issue.11, pp.929-934, 2000. ,
DOI : 10.1016/S0764-4442(00)01750-X
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
Semidefinite characterization and computation of zero-dimensional real radical ideals, Found, Comput. Math, vol.8, pp.607-647, 2008. ,
Positive Polynomials and Their Applications, 2009. ,
An Introduction to Polynomial and Semi-Algebraic Optimization, 2015. ,
DOI : 10.1017/CBO9781107447226
URL : https://hal.archives-ouvertes.fr/hal-02095856
Tractable approximations of sets defined with quantifiers, Mathematical Programming, vol.17, issue.2, pp.507-527, 2015. ,
DOI : 10.1137/050623802
Computing Gaussian & exponential measures of semi-algebraic sets, Advances in Applied Mathematics, vol.91, pp.137-163, 2017. ,
DOI : 10.1016/j.aam.2017.06.006
URL : https://hal.archives-ouvertes.fr/hal-01185641
Semidefinite Programming vs. LP Relaxations for Polynomial Programming, Mathematics of Operations Research, vol.27, issue.2, pp.347-360, 2002. ,
DOI : 10.1287/moor.27.2.347.322
Bounds on measures satisfying moment conditions, The Annals of Applied Probability, vol.12, issue.3, pp.1114-1137, 2002. ,
DOI : 10.1214/aoap/1031863183
Convergent SDP???Relaxations in Polynomial Optimization with Sparsity, SIAM Journal on Optimization, vol.17, issue.3, pp.822-843, 2006. ,
DOI : 10.1137/05064504X
Nonlinear Optimal Control via Occupation Measures and LMI-Relaxations, SIAM Journal on Control and Optimization, vol.47, issue.4, pp.47-1649, 2008. ,
DOI : 10.1137/070685051
URL : https://hal.archives-ouvertes.fr/hal-00136032
Inverse Polynomial Optimization, Mathematics of Operations Research, vol.38, issue.3, pp.418-436, 2013. ,
DOI : 10.1287/moor.1120.0578
URL : https://hal.archives-ouvertes.fr/hal-00577168
Geometric and Numerical Foundations of Movements, Advanced Robotics, vol.117, 2017. ,
DOI : 10.1007/978-3-319-51547-2
URL : https://hal.archives-ouvertes.fr/hal-01590779
A Comparison of the Sherali-Adams, Lov??sz-Schrijver, and Lasserre Relaxations for 0???1 Programming, Mathematics of Operations Research, vol.28, issue.3, pp.470-496, 2003. ,
DOI : 10.1287/moor.28.3.470.16391
Sums of Squares, Moment Matrices and Optimization Over Polynomials, Emerging Applications of Algebraic Geometry IMA Volumes in Mathematics and its Applications 149, pp.157-270, 2009. ,
DOI : 10.1007/978-0-387-09686-5_7
Sparsity-Exploiting Moment-Based Relaxations of the Optimal Power Flow Problem, IEEE Transactions on Power Systems, vol.30, issue.6, pp.3168-3180, 2015. ,
DOI : 10.1109/TPWRS.2014.2372478
A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations, New Journal of Physics, vol.10, issue.7, 2008. ,
DOI : 10.1088/1367-2630/10/7/073013
Squared Functional Systems and Optimization Problems, High Performance Optimization, pp.405-440, 2000. ,
DOI : 10.1007/978-1-4757-3216-0_17
Optimality conditions and finite convergence of Lasserre???s hierarchy, Mathematical Programming, vol.352, issue.2, pp.97-121, 2014. ,
DOI : 10.1090/cbms/097
Certifying convergence of Lasserre???s hierarchy via flat truncation, Mathematical Programming, vol.11, issue.12, pp.42-485, 2013. ,
DOI : 10.1080/10556789908805766
URL : http://arxiv.org/pdf/1106.2384
The $${\mathcal {A}}$$ A -Truncated $$K$$ K -Moment Problem, Foundations of Computational Mathematics, vol.14, issue.6, pp.1243-1276, 2014. ,
DOI : 10.1017/S0962492901000071
Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization, 2000. ,
Semidefinite programming relaxations for semialgebraic problems, Mathematical Programming, vol.96, issue.2, pp.293-320, 2003. ,
DOI : 10.1007/s10107-003-0387-5
URL : http://control.ee.ethz.ch/~parrilo/pubs/files/SDPrelaxations.ps.gz
Linear Conic Optimization for Inverse Optimal Control, SIAM Journal on Control and Optimization, vol.54, issue.3, pp.1798-1825, 2016. ,
DOI : 10.1137/14099454X
URL : https://hal.archives-ouvertes.fr/hal-01080428
Stability Analysis and Control of Rigid-Body Systems With Impacts and Friction, IEEE Transactions on Automatic Control, vol.61, issue.6, pp.1423-1437, 2016. ,
DOI : 10.1109/TAC.2015.2459151
Convergent Relaxations of Polynomial Optimization Problems with Noncommuting Variables, SIAM Journal on Optimization, vol.20, issue.5, pp.2157-2180, 2010. ,
DOI : 10.1137/090760155
Positive polynomials on compact semi-algebraic sets, Indiana Univ, Math. J, vol.42, pp.969-984, 1993. ,
DOI : 10.1016/s0764-4442(99)80251-1
The Moment problem, 2017. ,
DOI : 10.1007/978-3-319-64546-9
Computational Approaches to Lattice Packing and Covering Problems, Discrete & Computational Geometry, vol.35, issue.1, pp.73-116, 2006. ,
DOI : 10.1007/s00454-005-1202-2
Nondifferentiable Optimization and Polynomial Problems, 1988. ,
DOI : 10.1007/978-1-4757-6015-6
Spectral measures and moment problems, in Spectral Theory and Applications, Theta Ser, Theta, pp.173-215, 2003. ,
Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity, SIAM Journal on Optimization, vol.17, issue.1, pp.218-242, 2006. ,
DOI : 10.1137/050623802