F. Alizadeh, Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization, SIAM Journal on Optimization, vol.5, issue.1, pp.13-51, 1995.
DOI : 10.1137/0805002

H. H. Bauschke and J. M. Borwein, On the convergence of von Neumann's alternating projection algorithm for two sets, Set-Valued Analysis, vol.23, issue.3, pp.185-212, 1993.
DOI : 10.1007/BF01027691

R. Borsdorf and N. Higham, A preconditioned Newton algorithm for the nearest correlation matrix, IMA Journal of Numerical Analysis, vol.30, issue.1, 2008.
DOI : 10.1093/imanum/drn085

S. Boyd and L. Vandenberghe, Convex optimization, 2005.

S. Boyd and L. Xiao, Least-Squares Covariance Matrix Adjustment, SIAM Journal on Matrix Analysis and Applications, vol.27, issue.2, pp.532-546, 2005.
DOI : 10.1137/040609902

URL : http://authors.library.caltech.edu/1382/1/BOYsiamjmaa05.pdf

B. D. Craven and J. J. Koliha, Generalizations of Farkas??? Theorem, SIAM Journal on Mathematical Analysis, vol.8, issue.6, pp.983-997, 1977.
DOI : 10.1137/0508076

B. Dumitrescu, Positive trigonometric polynomials and signal processing applications, 2007.
DOI : 10.1007/978-3-319-53688-0

R. L. Dykstra, An Algorithm for Restricted Least Squares Regression, Journal of the American Statistical Association, vol.29, issue.384, pp.837-842, 1983.
DOI : 10.1080/01621459.1983.10477029

P. Gahinet and A. Nemirovski, The projective method for solving linear matrix inequalities, Mathematical Programming, vol.69, issue.1, pp.163-190, 1997.
DOI : 10.1007/BF02614434

J. V. Burke, A. S. Lewis, and M. L. Overton, HANSO: hybrid algorithm for nonsmooth optimization , a Matlab package based on BFGS, bundle and gradient sampling methods

J. V. Burke, D. Henrion, A. S. Lewis, and M. L. Overton, HIFOO - A MATLAB PACKAGE FOR FIXED-ORDER CONTROLLER DESIGN AND H??? OPTIMIZATION, Proc. IFAC Symp. Robust Control Design, 2006.
DOI : 10.3182/20060705-3-FR-2907.00059

M. D. Choi, T. Y. Lam, and B. Reznick, Sums of squares of real polynomials, Proc. Symp. Pure Math, pp.103-126, 1995.
DOI : 10.1090/pspum/058.2/1327293

F. Deutsch, Best approximation in inner product spaces, 2001.
DOI : 10.1007/978-1-4684-9298-9

L. Ghaoui and P. Gahinet, Rank minimization under LMI constraints: a framework for output feedback problems, Proc. Europ. Control. Conf, 1993.

M. Fazel, Matrix rank minimization with applications, 2002.

J. W. Helton and M. Putinar, Positive polynomials in scalar and matrix variables, the spectral theorem and optimization Operator theory, structured matrices and dilations: Tiberiu Constantinescu memorial volume. Theta Foundation, pp.229-306, 2007.

D. Henrion and J. B. Lasserre, GloptiPoly, ACM Transactions on Mathematical Software, vol.29, issue.2, pp.165-194
DOI : 10.1145/779359.779363

URL : https://hal.archives-ouvertes.fr/hal-00578944

D. Henrion and J. Malick, SDLS: a Matlab package for solving conic least-squares problems
URL : https://hal.archives-ouvertes.fr/hal-00172439

D. Henrion, J. B. Lasserre, and J. Löfberg, GloptiPoly 3: moments, optimization and semidefinite programming, Optimization Methods and Software, vol.24, issue.4-5
DOI : 10.1080/10556780802699201

URL : https://hal.archives-ouvertes.fr/hal-00172442

N. Higham, Computing a nearest symmetric positive semidefinite matrix, Linear Algebra and its Applications, vol.103, pp.103-118, 1988.
DOI : 10.1016/0024-3795(88)90223-6

N. Higham, Computing the nearest correlation matrix--a problem from finance, IMA Journal of Numerical Analysis, vol.22, issue.3, pp.329-343, 2002.
DOI : 10.1093/imanum/22.3.329

J. B. Hiriart-urruty and C. Lemaréchal, Convex analysis and minimization algorithms, 1993.
DOI : 10.1007/978-3-662-02796-7

F. Jarre and F. , An augmented primal-dual method for linear conic problems, 2007.

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

M. Laurent, Sums of squares, moment matrices and optimization over polynomials Emerging applications of algebraic geometry, Math. Appli, vol.149, pp.157-270, 2009.

A. Lewis and J. Malick, Alternating Projections on Manifolds, Mathematics of Operations Research, vol.33, issue.1, pp.216-234, 2008.
DOI : 10.1287/moor.1070.0291

URL : https://hal.archives-ouvertes.fr/hal-00317157

A. Lewis, R. Luke, and J. Malick, Local Linear Convergence for Alternating and Averaged Nonconvex Projections, Foundations of Computational Mathematics, vol.42, issue.3, 2008.
DOI : 10.1007/s10208-008-9036-y

J. Löfberg, Pre- and Post-Processing Sum-of-Squares Programs in Practice, IEEE Transactions on Automatic Control, vol.54, issue.5, 2008.
DOI : 10.1109/TAC.2009.2017144

J. Malick, A Dual Approach to Semidefinite Least-Squares Problems, SIAM Journal on Matrix Analysis and Applications, vol.26, issue.1, pp.272-284, 2004.
DOI : 10.1137/S0895479802413856

URL : https://hal.archives-ouvertes.fr/inria-00072409

H. D. Mittelmann, An independent benchmarking of SDP and SOCP solvers, Mathematical Programming, vol.95, issue.2, pp.407-430, 2003.
DOI : 10.1007/s10107-002-0355-5

B. N. Mordukhovich, Variational analysis and generalized differentiation, 2006.
DOI : 10.1007/3-540-31247-1

Y. Nesterov, Smooth minimization of non-smooth functions, Mathematical Programming, vol.269, issue.1, pp.127-152, 2005.
DOI : 10.1007/s10107-004-0552-5

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. Nocedal and S. J. Wright, Numerical optimization, 1999.
DOI : 10.1007/b98874

R. Orsi, U. Helmke, and J. B. Moore, A Newton-like method for solving rank constrained linear matrix inequalities, Automatica, issue.11, pp.421875-1882, 2006.

P. A. Parrilo, Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization, 2000.

H. Peyrl and P. A. Parrilo, Computing sum of squares decompositions with rational coefficients, Theoretical Computer Science, vol.409, issue.2, pp.269-281, 2008.
DOI : 10.1016/j.tcs.2008.09.025

V. Powers and T. Wörmann, An algorithm for sums of squares of real polynomials, Journal of Pure and Applied Algebra, vol.127, issue.1, pp.99-104, 1998.
DOI : 10.1016/S0022-4049(97)83827-3

H. Qi and D. Sun, A Quadratically Convergent Newton Method for Computing the Nearest Correlation Matrix, SIAM Journal on Matrix Analysis and Applications, vol.28, issue.2, pp.360-385, 2006.
DOI : 10.1137/050624509

M. A. Rami, U. Helmke, and J. B. Moore, A finite steps algorithm for solving convex feasibility problems, Journal of Global Optimization, vol.38, issue.1, pp.143-160, 2007.
DOI : 10.1007/s10898-006-9088-y

R. T. Rockafellar, Convex analysis, 1970.
DOI : 10.1515/9781400873173

A. Schrijver, Theory of linear and integer programming, 1986.

J. F. Sturm, Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones, Optimization Methods and Software, vol.81, issue.1-4, pp.11-12625, 1999.
DOI : 10.1287/moor.19.1.53

L. Tunçel and H. Wolkowicz, Strong duality and minimal representation for cone optimization, 2008.

R. H. Tütüncü, K. C. Toh, and M. J. Todd, Inexact primal-dual path-following algorithms for a special class of convex quadratic SDP and related problems, Pacific J. Optimization, vol.3, pp.135-164, 2007.

Z. Wang, S. Zheng, Y. Ye, and S. Boyd, Further Relaxations of the Semidefinite Programming Approach to Sensor Network Localization, SIAM Journal on Optimization, vol.19, issue.2, pp.655-673, 2008.
DOI : 10.1137/060669395

H. Wolkowicz, R. Saigal, and L. Vandenberghe, Handbook of semidefinite programming, 2000.
DOI : 10.1007/978-1-4615-4381-7