F. Capitanescu, J. L. Martinez-ramos, P. Panciatici, D. Kirschen, A. Marano-marcolini et al., State-of-the-art, challenges, and future trends in security constrained optimal power flow, Electric Power Systems Research, vol.81, issue.8, pp.1731-1741, 2011.
DOI : 10.1016/j.epsr.2011.04.003

M. J. Carpentier, Contribution à l'étude du dispatching économique, pp.431-447, 1962.

E. De-klerk, Aspects of Semidefinite Programming -Interior Point Algorithms and Selected Applications, p.24, 2002.

C. Ferrier, Hilbert???s 17th problem and best dual bounds in quadratic minimization, Cybernetics and Systems Analysis, vol.2, issue.5, pp.696-709, 1998.
DOI : 10.1007/BF02667043

J. Ch and . Gilbert, Step by step design of an interior point solver in self-dual conic optimization ? Application to the Shor relaxation of some small OPF problems. Lecture notes of the Master-2 " Optimization, p.38, 2016.

J. Ch and . Gilbert, On the equivalence between R-linear and C-linear systems of equations in complex numbers, INRIA-Paris, 2 rue Simone Iff, p.75589, 2017.

J. Ch and . Gilbert, Convergence of a feasible predictor-corrector interior-point algorithm for the semidefinite optimization problem in complex numbers, p.29, 2017.

J. Ch, C. Gilbert, and . Josz, Plea for a semidefinite optimization solver in complex numbers, 2017.

M. X. Goemans and D. P. Williamson, Approximation algorithms for MAX-3-CUT and other problems via complex semidefinite programming, Proceedings of the thirty-third annual ACM symposium on Theory of computing , STOC '01, pp.442-470, 2004.
DOI : 10.1145/380752.380838

URL : http://doi.org/10.1016/j.jcss.2003.07.012

N. J. Higham, Accuracy and Stability of Numerical Algorithms (second edition), 2002.

N. J. Higham, Cholesky factorization, Wiley Interdisciplinary Reviews: Computational Statistics, vol.103, issue.2, pp.251-254, 2009.
DOI : 10.1002/wics.18

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.662.881

J. Hiriart-urruty and C. , Convex Analysis and Minimization Algorithms. Grundlehren der mathematischen Wissenschaften 305-306, 1993.
DOI : 10.1007/978-3-662-02796-7

W. Huang, K. Gallivan, and X. Zhang, Solving PhaseLift by low-rank Riemannian optimization methods for complex semidefinite constraints, 2016.
DOI : 10.1016/j.procs.2016.05.422

URL : http://doi.org/10.1016/j.procs.2016.05.422

J. Jiang, A long-step primal???dual path-following method for semidefinite programming, Operations Research Letters, vol.23, issue.1-2, pp.53-62, 1998.
DOI : 10.1016/S0167-6377(98)00018-2

C. Josz, Application of Polynomial Optimization to Electricity Transmission Networks, 2016.
URL : https://hal.archives-ouvertes.fr/tel-01478431

C. Josz, S. Fliscounakis, J. Maeght, and P. Panciatici, AC power flow data in MATPOWER and QCQP format: iTesla, RTE snapshots, and PEGASE, p.40, 2016.

C. Josz, J. Maeght, P. Panciatici, J. Ch, and . Gilbert, Application of the Moment-SOS Approach to Global Optimization of the OPF Problem, IEEE Transactions on Power Systems, vol.30, issue.1, pp.463-470, 2015.
DOI : 10.1109/TPWRS.2014.2320819

URL : https://hal.archives-ouvertes.fr/hal-00906483

C. Josz and D. K. Molzahn, Moment/sum-of-squares hierarchy for complex polynomial optimization, SIAM Journal on Optimization, vol.4, p.12, 2015.

M. Kojima, S. Shindoh, and S. Hara, Interior-Point Methods for the Monotone Semidefinite Linear Complementarity Problem in Symmetric Matrices, SIAM Journal on Optimization, vol.7, issue.1, pp.86-125, 1997.
DOI : 10.1137/S1052623494269035

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, Convergent LMI relaxations for nonconvex quadratic programs Graduate seminar at MIT, fall, 2001.
DOI : 10.1109/cdc.2001.914738

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.26.5707

J. B. Lasserre, An Introduction to Polynomial and Semi-Algebraic Optimization. Cambridge Texts in Applied Mathematics, 2015.
DOI : 10.1017/cbo9781107447226

J. Lavaei and S. H. Low, Zero Duality Gap in Optimal Power Flow Problem, IEEE Transactions on Power Systems, vol.27, issue.1, pp.92-107, 2012.
DOI : 10.1109/TPWRS.2011.2160974

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.363.3331

S. H. Low, Convex Relaxation of Optimal Power Flow—Part I: Formulations and Equivalence, IEEE Transactions on Control of Network Systems, vol.1, issue.1, pp.15-27, 2014.
DOI : 10.1109/TCNS.2014.2309732

S. H. Low, Convex Relaxation of Optimal Power Flow—Part II: Exactness, IEEE Transactions on Control of Network Systems, vol.1, issue.2, pp.177-189, 2014.
DOI : 10.1109/TCNS.2014.2323634

S. Mehrotra, On the Implementation of a Primal-Dual Interior Point Method, SIAM Journal on Optimization, vol.2, issue.4, pp.575-601, 1992.
DOI : 10.1137/0802028

S. Mizuno, M. J. Todd, and Y. Ye, On Adaptive-Step Primal-Dual Interior-Point Algorithms for Linear Programming, Mathematics of Operations Research, vol.18, issue.4, pp.964-981, 1993.
DOI : 10.1287/moor.18.4.964

URL : http://ecommons.cornell.edu/bitstream/1813/8829/1/TR000944.pdf

D. K. Molzahn and I. A. Hiskens, Moment-based relaxation of the optimal power flow problem, 2014 Power Systems Computation Conference, 2013.
DOI : 10.1109/PSCC.2014.7038397

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

Y. E. Nesterov and M. J. Todd, Self-Scaled Barriers and Interior-Point Methods for Convex Programming, Mathematics of Operations Research, vol.22, issue.1, pp.1-42, 1997.
DOI : 10.1287/moor.22.1.1

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

R. T. Rockafellar, Convex Analysis, Princeton Mathematics Ser, vol.28, 1970.
DOI : 10.1515/9781400873173

C. Roos, T. Terlaky, and J. , Theory and Algorithms for Linear Optimization ? An Interior Point Approach, Vial, p.23, 1997.

. Sedumi, Internet site http://sedumi.ie.lehigh, p.43

N. Z. Shor, Quadratic optimization problems, Soviet Journal of Computer and System Sciences, vol.25, issue.251 4, pp.1-11, 1987.

L. Sorber, M. Van-barel, and L. De-lathauwer, Unconstrained Optimization of Real Functions in Complex Variables, SIAM Journal on Optimization, vol.22, issue.3, pp.879-898, 2012.
DOI : 10.1137/110832124

J. F. Sturm, Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetric cones. Optimization Methods and Software, pp.625-653, 1999.
DOI : 10.1080/10556789908805766

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.6954

K. Toh, M. J. Todd, and R. H. Tütüncü, On the Implementation and Usage of SDPT3 ??? A Matlab Software Package for Semidefinite-Quadratic-Linear Programming, Version 4.0, Handbook on Semidefinite, Conic and Polynomial Optimization , International Series in Operations Research and Management Science 166, pp.715-754, 2012.
DOI : 10.1007/978-1-4614-0769-0_25

K. Toh, R. H. Tütüncü, and M. J. Todd, On the implementation and usage of SDPT3 -a Matlab software package for semidefinite-quadratic-linear programming, version 4.0. Technical report. User's guide of SDPT3, p.39, 2006.

L. Vandenberghe and S. Boyd, Semidefinite Programming, SIAM Review, vol.38, issue.1, pp.49-95, 1996.
DOI : 10.1137/1038003

I. Waldspurger, A. Aspremont, and S. Mallat, Phase recovery, MaxCut and complex semidefinite programming, Mathematical Programming, vol.16, issue.3, pp.47-81, 2015.
DOI : 10.1007/s10107-013-0738-9

URL : https://hal.archives-ouvertes.fr/hal-00907535

J. Watrous, Simpler semidefinite programs for completely bounded norms, Chicago Journal of Theoretical Computer Science. Article, vol.8, issue.3, 2013.

R. D. Zimmerman, C. E. Murillo-sánchez, and R. J. Thomas, MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education, IEEE Transactions on Power Systems, vol.26, issue.1, pp.12-19, 2011.
DOI : 10.1109/TPWRS.2010.2051168

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.378.1509