M. F. Anjos and J. B. Lasserre, Introduction to Semidefinite, Conic and Polynomial Optimization, Handbook on Semidefinite, Conic and Polynomial Optimization of International Series in Operations Research & Management Science, 2012.
DOI : 10.1007/978-1-4614-0769-0_1

X. Bai, H. Wei, K. Fujisawa, and Y. Wang, Semidefinite programming for optimal power flow problems, International Journal of Electrical Power & Energy Systems, vol.30, issue.6-7, pp.6-7, 2008.
DOI : 10.1016/j.ijepes.2007.12.003

A. Ben-tal and A. Nemirovski, Lectures on Modern Convex Optimization ? Analysis, Algorithms, and Engineering Applications, MPS-SIAM Series on Optimization 2. SIAM. 3, 2001.
DOI : 10.1137/1.9780898718829

G. Blekherman, P. A. Parrilo, and R. R. Thomas, Semidefinite Optimization and Convex Algebraic Geometry, MOS-SIAM Series on Optimization. SIAM and MPS, issue.8, 2013.
DOI : 10.1137/1.9781611972290

J. F. Bonnans, J. Ch, C. Gilbert, C. Lemaréchal, and . Sagastizábal, Numerical Optimization ? Theoretical and Practical Aspects (second edition). Universitext, 2006.

S. Bose, D. F. Gayme, K. M. Chandy, and S. H. Low, Quadratically Constrained Quadratic Programs on Acyclic Graphs With Application to Power Flow, IEEE Transactions on Control of Network Systems, vol.2, issue.3, p.13, 2012.
DOI : 10.1109/TCNS.2015.2401172

S. Bose, D. F. Gayme, S. H. Low, and K. M. Chandy, Optimal power flow over tree networks, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton), p.13, 2011.
DOI : 10.1109/Allerton.2011.6120323

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.452.990

W. A. Bukhsh, A. Grothey, K. I. Mckinnon, and P. A. Trodden, Local Solutions of the Optimal Power Flow Problem, IEEE Transactions on Power Systems, vol.28, issue.4, p.14, 2013.
DOI : 10.1109/TPWRS.2013.2274577

W. A. Bukhsh, A. Grothey, K. I. Mckinnon, and P. A. Trodden, Test case archive of optimal power flow (OPF) problem with local optima Available online, p.14, 2013.

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

E. De-klerk and M. Laurent, On the Lasserre Hierarchy of Semidefinite Programming Relaxations of Convex Polynomial Optimization Problems, SIAM Journal on Optimization, vol.21, issue.3, pp.824-832, 2011.
DOI : 10.1137/100814147

M. Farivar and S. Low, Branch Flow Model: Relaxations and Convexification???Part II, IEEE Transactions on Power Systems, vol.28, issue.3, pp.2565-2572, 2013.
DOI : 10.1109/TPWRS.2013.2255318

A. Gopalakrishnan, A. U. Raghunathan, D. Nikovski, and L. T. Biegler, Global optimization of Optimal Power Flow using a branch & bound algorithm, 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2012.
DOI : 10.1109/Allerton.2012.6483274

D. Henrion, J. B. Lasserre, and J. Löfberg, GloptiPoly 3: moments, optimization and semidefinite programming. Optimization Methods and Software, pp.761-779, 2009.
DOI : 10.1080/10556780802699201

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

M. Huneault and F. D. Galiana, A survey of the optimal power flow literature, IEEE Transactions on Power Systems, vol.6, issue.2, pp.762-770, 1991.
DOI : 10.1109/59.76723

P. Kundur, AC transmission, Power System Stability and Control, pp.245-249, 1994.

J. B. Lasserre, Convergent LMI relaxations for nonconvex quadratic programs, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)
DOI : 10.1109/CDC.2001.914738

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

J. B. Lasserre, 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

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, Moments Positive Polynomials and Their Applications. Imperial College Press Optimization Series 1, 2010.
DOI : 10.1142/p665

J. B. Lasserre, Convexity in SemiAlgebraic Geometry and Polynomial Optimization, SIAM Journal on Optimization, vol.19, issue.4, pp.1995-2014, 2008.
DOI : 10.1137/080728214

URL : http://arxiv.org/abs/0806.3784

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

B. C. Lesieutre, D. K. Molzahn, A. R. Borden, and C. L. Demarco, Examining the limits of the application of semidefinite programming to power flow problems, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pp.28-30, 2011.
DOI : 10.1109/Allerton.2011.6120344

J. Löfberg, YALMIP : a toolbox for modeling and optimization in MATLAB, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508), pp.284-289, 2004.
DOI : 10.1109/CACSD.2004.1393890

Z. Luo, W. Ma, A. M. So, Y. Ye, and S. Zhang, Semidefinite Relaxation of Quadratic Optimization Problems, IEEE Signal Processing Magazine, vol.27, issue.3, pp.20-34, 2010.
DOI : 10.1109/MSP.2010.936019

K. S. Pandya and S. K. Joshi, A survey of optimal power flow methods, Journal of Theoretical of Applied Information Technology, vol.4, issue.5, pp.450-458, 2008.

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

M. Putinar and K. Schmüdgen, Multivariate determinates, Indiana University Mathematics Journal, vol.57, issue.6, pp.2931-2968, 2008.
DOI : 10.1512/iumj.2008.57.3692

URL : http://doi.org/10.1512/iumj.2008.57.3692

R. T. Rockafellar, Conjugate Duality and Optimization, Regional Conference Series in Applied Mathematics 16. SIAM, 1974.
DOI : 10.1137/1.9781611970524

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.298.6548

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

S. Sojoudi and J. Lavaei, Network topologies guaranteeing zero duality gap for optimal power flow problem, p.6, 2012.

S. Sojoudi and J. Lavaei, Physics of power networks makes hard optimization problems easy to solve, 2012 IEEE Power and Energy Society General Meeting, p.13, 2012.
DOI : 10.1109/PESGM.2012.6345272

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

J. F. Sturm and S. Zhang, On Cones of Nonnegative Quadratic Functions, Mathematics of Operations Research, vol.28, issue.2, pp.246-267, 2003.
DOI : 10.1287/moor.28.2.246.14485

H. Wolkowicz, R. Saigal, and L. Vandenberghe, Handbook of Semidefinite Programming ? Theory, Algorithms, and Applications, 2000.

B. Zhang and D. Tse, Geometry of feasible injection region of power networks, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton), p.13, 2011.
DOI : 10.1109/Allerton.2011.6120346

R. Zimmerman, C. Murillo-sánchez, and R. 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.1-8, 2011.
DOI : 10.1109/TPWRS.2010.2051168