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A hydrothermal problem with non-smooth Lagrangian
1. | University of Oviedo, Department of Mathematics, E.P.I, Campus of Viesques, Gijón, 33203, Spain, Spain, Spain, Spain |
References:
[1] |
N. Amjady and H. Nasiri-Rad, Solution of nonconvex and nonsmooth economic dispatch by a new Adaptive Real Coded Genetic Algorithm, Expert Syst. Appl., 37 (2010), 5239-5245.
doi: 10.1016/j.eswa.2009.12.084. |
[2] |
L. Bayón, J. M. Grau, M. M. Ruiz and P. M. Suárez, Nonsmooth Optimization of Hydrothermal Problems, J. Comput. Appl. Math., 192 (2006), 11-19.
doi: 10.1016/j.cam.2005.04.048. |
[3] |
L. Bayón, J. M. Grau, M. M. Ruiz and P. M. Suárez, An optimization problem in deregulated electricity markets solved with the nonsmooth maximum principle, Int. J. Comput. Math., 86 (2009), 237-249.
doi: 10.1080/00207160701864483. |
[4] |
L. Bayón, J. Grau, M. M. Ruiz and P.M. Suárez, A Constrained and Nonsmooth Hydrothermal Problem, Appl. Math. Comput., 209 (2009), 10-18.
doi: 10.1016/j.amc.2008.06.013. |
[5] |
L. Bayón, J. M. Grau, M. M. Ruiz and P. M. Suárez, Algorithm for calculating the analytic solution for economic dispatch with multiple fuel units, Comput. Math. Appl., 62 (2011), 2225-2234.
doi: 10.1016/j.camwa.2011.07.008. |
[6] |
C. L. Chiang, Genetic algorithm for static power economic dispatch, Computer Science and Information Engineering, 2009 WRI World Congress (2009), 646-650.
doi: 10.1109/CSIE.2009.440. |
[7] |
F. H. Clarke, Optimization and Nonsmooth Analysis, John Wiley & Sons, New York, 1983. |
[8] |
L. S. Coelho and V. C. Mariani, Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect, IEEE Trans. Power Syst., 21 (2006), 989-996. |
[9] |
A. D. Ioffe and R. T. Rockafellar, The Euler and Weierstrass conditions for nonsmooth variational problems, Calc. Var. Partial Dif., 4 (1996), 59-87.
doi: 10.1007/BF01322309. |
[10] |
D. Liu and Y. Cai, Taguchi method for solving the economic dispatch problem with nonSmooth cost functions, IEEE Trans. Power Syst., 20 (2005), 2006-2014.
doi: 10.1109/TPWRS.2005.857939. |
[11] |
P. D. Loewen and R. T. Rockafellar, New necessary conditions for the generalized problem of Bolza, SIAM J. Control Optim., 34 (1996), 1496-1511.
doi: 10.1137/S0363012994275932. |
[12] |
C. Marcelli, Variational problems with nonconvex, noncoercive, highly discontinuous integrands: characterization and existence of minimizers, SIAM J. Control Optim., 40 (2002), 1473-1490.
doi: 10.1137/S036301299936141X. |
[13] |
C. Marcelli, E. Outkine and M. Sytchev, Remarks on necessary conditions for minimizers of one-dimensional variational problems, Nonlinear Anal., 48 (2002), 979-993.
doi: 10.1016/S0362-546X(00)00228-5. |
[14] |
J. B. Park, K. S. Lee, J. R. Shin and K. Y. Lee, A particle swarm optimization for economic dispatch with nonsmooth cost functions, IEEE Trans. Power Syst., 20 (2005), 34-42.
doi: 10.1109/TPWRS.2004.831275. |
[15] |
J. L. Troutman, Variational Calculus with Elementary Convexity, Springer, New York, 1983. |
[16] |
M. T. Tsai, H. J. Gow and W. M. Lin, A novel stochastic search method for the solution of economic dispatch problems with non-convex fuel cost functions, Int. J. Elec. Power, 33 (2011), 1070-1076.
doi: 10.1016/j.ijepes.2011.01.026. |
[17] |
R. Vinter and H. Zheng, The extended Euler-Lagrange condition for nonconvex variational problems, SIAM J. Control Optim., 35 (1997), 56-77.
doi: 10.1137/S0363012995283133. |
[18] |
A. J. Wood and B. F. Wollenberg, Power Generation, Operation, and Control, Wiley-Interscience, 1996.
doi: 10.1016/0140-6701(96)88715-7. |
[19] |
X. Yuan, L. Wang, Y. Zhang and Y. Yuan, A hybrid differential evolution method for dynamic economic dispatch with valve-point effects, Expert Syst. Appl., 36 (2009), 4042-4048.
doi: 10.1016/j.eswa.2008.03.006. |
[20] |
K. Zare, M. T. Haque and E. Davoodi, Solving non-convex economic dispatch problem with valve point effects using modified group search optimizer method, Electr. Pow. Syst. Res., 84 (2012), 83-89.
doi: 10.1016/j.epsr.2011.10.004. |
show all references
References:
[1] |
N. Amjady and H. Nasiri-Rad, Solution of nonconvex and nonsmooth economic dispatch by a new Adaptive Real Coded Genetic Algorithm, Expert Syst. Appl., 37 (2010), 5239-5245.
doi: 10.1016/j.eswa.2009.12.084. |
[2] |
L. Bayón, J. M. Grau, M. M. Ruiz and P. M. Suárez, Nonsmooth Optimization of Hydrothermal Problems, J. Comput. Appl. Math., 192 (2006), 11-19.
doi: 10.1016/j.cam.2005.04.048. |
[3] |
L. Bayón, J. M. Grau, M. M. Ruiz and P. M. Suárez, An optimization problem in deregulated electricity markets solved with the nonsmooth maximum principle, Int. J. Comput. Math., 86 (2009), 237-249.
doi: 10.1080/00207160701864483. |
[4] |
L. Bayón, J. Grau, M. M. Ruiz and P.M. Suárez, A Constrained and Nonsmooth Hydrothermal Problem, Appl. Math. Comput., 209 (2009), 10-18.
doi: 10.1016/j.amc.2008.06.013. |
[5] |
L. Bayón, J. M. Grau, M. M. Ruiz and P. M. Suárez, Algorithm for calculating the analytic solution for economic dispatch with multiple fuel units, Comput. Math. Appl., 62 (2011), 2225-2234.
doi: 10.1016/j.camwa.2011.07.008. |
[6] |
C. L. Chiang, Genetic algorithm for static power economic dispatch, Computer Science and Information Engineering, 2009 WRI World Congress (2009), 646-650.
doi: 10.1109/CSIE.2009.440. |
[7] |
F. H. Clarke, Optimization and Nonsmooth Analysis, John Wiley & Sons, New York, 1983. |
[8] |
L. S. Coelho and V. C. Mariani, Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect, IEEE Trans. Power Syst., 21 (2006), 989-996. |
[9] |
A. D. Ioffe and R. T. Rockafellar, The Euler and Weierstrass conditions for nonsmooth variational problems, Calc. Var. Partial Dif., 4 (1996), 59-87.
doi: 10.1007/BF01322309. |
[10] |
D. Liu and Y. Cai, Taguchi method for solving the economic dispatch problem with nonSmooth cost functions, IEEE Trans. Power Syst., 20 (2005), 2006-2014.
doi: 10.1109/TPWRS.2005.857939. |
[11] |
P. D. Loewen and R. T. Rockafellar, New necessary conditions for the generalized problem of Bolza, SIAM J. Control Optim., 34 (1996), 1496-1511.
doi: 10.1137/S0363012994275932. |
[12] |
C. Marcelli, Variational problems with nonconvex, noncoercive, highly discontinuous integrands: characterization and existence of minimizers, SIAM J. Control Optim., 40 (2002), 1473-1490.
doi: 10.1137/S036301299936141X. |
[13] |
C. Marcelli, E. Outkine and M. Sytchev, Remarks on necessary conditions for minimizers of one-dimensional variational problems, Nonlinear Anal., 48 (2002), 979-993.
doi: 10.1016/S0362-546X(00)00228-5. |
[14] |
J. B. Park, K. S. Lee, J. R. Shin and K. Y. Lee, A particle swarm optimization for economic dispatch with nonsmooth cost functions, IEEE Trans. Power Syst., 20 (2005), 34-42.
doi: 10.1109/TPWRS.2004.831275. |
[15] |
J. L. Troutman, Variational Calculus with Elementary Convexity, Springer, New York, 1983. |
[16] |
M. T. Tsai, H. J. Gow and W. M. Lin, A novel stochastic search method for the solution of economic dispatch problems with non-convex fuel cost functions, Int. J. Elec. Power, 33 (2011), 1070-1076.
doi: 10.1016/j.ijepes.2011.01.026. |
[17] |
R. Vinter and H. Zheng, The extended Euler-Lagrange condition for nonconvex variational problems, SIAM J. Control Optim., 35 (1997), 56-77.
doi: 10.1137/S0363012995283133. |
[18] |
A. J. Wood and B. F. Wollenberg, Power Generation, Operation, and Control, Wiley-Interscience, 1996.
doi: 10.1016/0140-6701(96)88715-7. |
[19] |
X. Yuan, L. Wang, Y. Zhang and Y. Yuan, A hybrid differential evolution method for dynamic economic dispatch with valve-point effects, Expert Syst. Appl., 36 (2009), 4042-4048.
doi: 10.1016/j.eswa.2008.03.006. |
[20] |
K. Zare, M. T. Haque and E. Davoodi, Solving non-convex economic dispatch problem with valve point effects using modified group search optimizer method, Electr. Pow. Syst. Res., 84 (2012), 83-89.
doi: 10.1016/j.epsr.2011.10.004. |
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