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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 376546, 26 pages
Predictor-Corrector Primal-Dual Interior Point Method for Solving Economic Dispatch Problems: A Postoptimization Analysis
1Department of Mathematics, Universidade Estadual Paulista (UNESP), 17033-360 Bauru, SP, Brazil
2Graduate Program in Electrical Engineering, Universidade Estadual Paulista (UNESP), 17033-360 Bauru, SP, Brazil
3Department of Electrical Engineering, UNESP—Universidade Estadual Paulista, 17033-360 Bauru, SP, Brazil
Received 9 November 2011; Accepted 3 April 2012
Academic Editor: Jianming Shi
Copyright © 2012 Antonio Roberto Balbo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- N. Karmarkar, “A new polynomial-time algorithm for linear programming,” Combinatorica, vol. 4, no. 4, pp. 373–395, 1984.
- I. I. Dikin, “Iterative solution of problems of linear and quadratic programming,” Doklady Akademii Nauk SSSR, vol. 174, pp. 747–748, 1967 (Russian).
- E. R. Barnes, “A variation on Karmarkar's algorithm for solving linear programming problems,” Mathematical Programming, vol. 36, no. 2, pp. 174–182, 1986.
- R. J. Vanderbei, M. S. Meketon, and B. A. Freedman, “A modification of Karmarkar's linear programming algorithm,” Algorithmica, vol. 1, no. 4, pp. 395–407, 1986.
- I. Adler, M. G. C. Resende, G. Veiga, and N. Karmarkar, “An implementation of Karmarkar's algorithm for linear programming,” Mathematical Programming, vol. 44, no. 1–3, pp. 297–335, 1989.
- A. R. Balbo, M. A. S. Souza, and E. C. Baptista, “Métodos primal-dual de pontos interiores aplicados à resolução de problemas de despacho econômico: sobre a influência da solução inicial,” in Proceedings of the Simpósio Brasileiro de Pesquisa Operacional, João Pessoa—Pb. Anais do XL SBPO (XL SBPO '08), pp. 2074–2085, ILTC, Rio de Janeiro, RJ, Brazil, 2008.
- N. Megiddo and M. Shub, “Boundary behavior of interior point algorithms in linear programming,” Mathematics of Operations Research, vol. 14, no. 1, pp. 97–146, 1989.
- A. V. Fiacco and G. P. McCormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley & Sons, New York, NY, USA, 1968.
- A. V. Fiacco and G. P. McCormick, Nonlinear Programming, vol. 4 of Classics in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 2nd edition, 1990.
- K. R. Frisch, The Logarithmic Potential Method of Convex Programming, University Institute of Economics, Oslo, Norway, 1955.
- P. E. Gill, W. Murray, M. A. Saunders, J. A. Tomlin, and M. H. Wright, “On projected Newton barrier methods for linear programming and an equivalence to Karmarkar's projective method,” Mathematical Programming, vol. 36, no. 2, pp. 183–209, 1986.
- Y. Ye, “An potential reduction algorithm for linear programming,” in Contemporary Mathematics, vol. 114, pp. 91–107, American Mathematical Society, Providence, RI, USA, 1990.
- J. Renegar, “A polynomial-time algorithm, based on Newton's method, for linear programming,” Mathematical Programming, vol. 40, no. 1, pp. 59–93, 1988.
- P. M. Vaidya, “An algorithm for linear programming which requires arithmetic operations,” Mathematical Programming, vol. 47, no. 2, pp. 175–201, 1990.
- N. Megiddo, “On the complexity of linear programming,” in Advances in Economic Theory, T. Bewley, Ed., pp. 225–268, Cambridge University Press, Cambridge, UK, 1989.
- C. C. Gonzaga, “An algorithm for solving linear programming problems in operations,” in Progress in Mathematical Programming: Interior-Point and Related Methods, N. Megiddo, Ed., pp. 1–28, Springer, New York, NY, USA, 1989.
- C. C. Gonzaga, “Polynomial affine algorithms for linear programming,” Mathematical Programming, vol. 49, no. 1, pp. 7–21, 1990.
- R. D. C. Monteiro and I. Adler, “Interior path following primal-dual algorithms. I. Linear programming,” Mathematical Programming, vol. 44, no. 1, pp. 27–41, 1989.
- R. D. C. Monteiro, I. Adler, and M. G. C. Resende, “A polynomial-time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extension,” Mathematics of Operations Research, vol. 15, no. 2, pp. 191–214, 1990.
- M. Kojima, S. Mizuno, and A. Yoshise, “A primal-dual interior point algorithm for linear programming,” in Progress in mathematical programming: Interior-Point and Related Methods, N. Megiddo, Ed., pp. 29–47, Springer, New York, NY, USA, 1989.
- S. Mehrotra and J. Sun, “An algorithm for convex quadratic programming that requires arithmetic operations,” Mathematics of Operations Research, vol. 15, no. 2, pp. 342–363, 1990.
- I. J. Lustig, R. E. Marsten, and D. F. Shanno, “On implementing Mehrotra's predictor-corrector interior-point method for linear programming,” SIAM Journal on Optimization, vol. 2, no. 3, pp. 435–449, 1992.
- Y. C. Wu, A. S. Debs, and R. E. Marsten, “Direct nonlinear predictor-corrector primal-dual interior point algorithm for optimal power flows,” IEEE Transactions on Power Systems, vol. 9, no. 2, pp. 876–883, 1994.
- S. C. Fang and S. Puthenpura, Linear Optimization and Extensions: Theory and Algorithms, Prentice-Hall, Englewood Cliffs, NJ, USA, 1993.
- J. O. Kim, D. J. Shin, J. N. Park, and C. Singh, “Atavistic genetic algorithm for economic dispatch with valve point effect,” Electric Power Systems Research, vol. 62, no. 3, pp. 201–207, 2002.
- N. M. Rodrigues, Um algoritmo cultural para problemas de despacho de energia elétrica, Dissertação de Mestrado, Universidade Estadual de Maringá, 2007.
- M. M. A. Samed, Um algoritmo genético Hibrido co-evolutivo para resolver problemas de despacho, Tese de Doutorado, UEM, Departamento de Engenharia Química, 2004.
- H. H. Happ, “Optimal power dispatch—a comprehensive survey,” IEEE Transactions on Power Apparatus and Systems, vol. 96, no. 3, pp. 841–854, 1977.
- M. J. C. Steinberg and T. H. Smith, Economic Loading of Power Plants and Electric Systems, MacGraw-Hill, 1943.
- A. R. L. Oliveira, S. Soares, and L. Nepomuceno, “Optimal active power dispatch combining network flow and interior point approaches,” IEEE Transactions on Power Systems, vol. 18, no. 4, pp. 1235–1240, 2003.
- M. S. Bazaraa, H. D. Sherali, and C. M. Shetty, Non Linear Programming-Theory and Algorithm, John Wiley & Sons, New York, NY, USA, 2nd edition, 1993.
- S. J. Wright, Primal-Dual Interior-Point Methods, SIAM, Philadelphia, Pa, USA, 1997.