Semidefinite programming for optimal power flow problems

Carpentier, 1962, Contribution á létude de Dispatching Economique, Bull Soc Fr Electric, 3, 431 Dommelll, 1968, Optimal power flow solutions, IEEE Trans PAS, 87, 1866, 10.1109/TPAS.1968.292150 Momoh, 1997, Challenges to optimal power flow, IEEE Trans Power Syst, 12, 444, 10.1109/59.575768 Granville, 1994, Optimal reactive dispatch through interior point methods, IEEE Trans Power Syst, 9, 136, 10.1109/59.317548 Wei, 1996, An application of interior point quadratic programming algorithm to power system optimization problems, IEEE Trans Power Syst, 11, 260, 10.1109/59.486104 Wu Y-C, Debs AS, Marsten RE. A direct nonlinear predictor-corrector primal–dual interior point algorithm for optimal power flows. Presented at power industry computer application conference, Scottsdale, AZ, USA; 1993. Quintana, 2000, Interior-point methods and their applications to power systems: a classification of publications, IEEE Trans Power Syst, 15, 170, 10.1109/59.852117 Adler I, Alizadeh F. Primal–dual interior point algorithms for convex quadratically constrained and semidefinite optimization problems. Technical report, Rutcor, Rutgers University, New Brunswick, NJ; 1995. Todd, 2001, Semidefinite optimization, Acta Numer, 10, 515, 10.1017/S0962492901000071 Mittelmann, 2003, An independent benchmarking of SDP and SOCP solvers, Math Program, B, 407, 10.1007/s10107-002-0355-5 Wolkowicz, 2001 P. Parrilo. Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. PhD thesis. California: Caltech, Pasadena; 2000. Parrilo, 2003, Semidefinite programming relaxations and algebraic optimization in control, Eur J Control, 9, 307, 10.3166/ejc.9.307-321 Alkire B, Vandenberghe L. Handling nonnegative constraints in spectral estimation. Technical report, Electrical Engineering Department, UCLA, Los Angeles, CA; 2000. Alkire B, Vandenberghe L.Convex optimization problems involving finite autocorrelation sequences. Technical report, Electrical Engineering Department, UCLA, Los Angeles, CA; 2001. Xiao L, Boyd S. Fast linear iterations for distributed averaging. Technical report, Stanford University, Stanford, CA; 2003. Benson, 2000, Solving large scale sparse semidefinite programs for combinatorial optimization, SIAM J Optim, 10, 443, 10.1137/S1052623497328008 Goemans, 1997, Semidefinite programming in combinatorial optimization, Math Program, 79, 143, 10.1007/BF02614315 Goemans MX. Semidefinite programming and combinatorial optimization. Documenta mathematica, Extra Volume ICM 1998. p. 657–66. Fuentes-Loyola, 2003, Medium-term hydrothermal coordination by semidefinite programming, IEEE Trans Power Syst, 18, 1515, 10.1109/TPWRS.2003.811006 Madrigal M, Quintana VH. Semidefinite programming relaxations for {0,l}-power dispatch problems. Presented at proceeding of IEEE-PES 1999 Summer Meeting, Edmonton, Al., Canada; 1999. Jabr, 2003, A primal–dual interior-point method to solve the optimal power flow dispatching problem, Optim Eng, 4, 309, 10.1023/B:OPTE.0000005390.63406.1e Alizadeh F, Haeberly J-PA, Overton ML. Primal–dual interior-point methods for semidefinite programming: convergence rates, stability and numerical results. Computer Science Department, Technical Report 721, New York University, May 31; 1996. Wei, 1998, A interior point nonlinear programming for optimal power flow problems with a novel data structure, IEEE Trans Power Syst, 13, 870, 10.1109/59.708745 Mizuno, 1995, Infeasible-interior-point primal–dual potential reduction algorithms for linear programming, SIAM J Optim, 5, 52, 10.1137/0805003 Alizadeh F. Combinatorial optimization with interior point methods and semidefinite matrices. PhD Thesis, University of Minnesota; 1991. Wright S. Primal–dual interior-point methods. Publisher: Soc for Industrial & Applied Math, June 1997. Fujisawa K, Fukuda M, Kojima M, Nakata K. Numerical evaluation of SDPA (Semidefinite Programming Algorithm). Technical report series B: operations research, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, September 1998. Yamashita, 2003, SDPARA: SemiDefinite programming algorithm PARAllel version, Parallel Comput, 29, 1053, 10.1016/S0167-8191(03)00087-5 Satoshi Matsuyama SN, Katsuki Fujisawa, Kazuhide Nakata, Masakazu Kojima. SDPA-M (SemiDefinite Programming Algorithm in MATLAB) user’s manual — Version 1.00. Technical report series B: operations research, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, January 2000. Lov’asz, 1991, Cones of matrices and set-functions and 0–1 optimization, SIAM J Optim, 1, 166, 10.1137/0801013 Fujisawa, 1997, Exploiting sparsity in primal–dual interior-point methods for semidefinite programming, Math Program, 79, 235, 10.1007/BF02614319 Wei, 2000, Large scale hydrothermal optimal power flow problems based on interior point nonlinear programming, IEEE Trans Power Syst, 15, 396, 10.1109/59.852150