Journal Menu

- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents

Mathematical Problems in Engineering

Volume 2012 (2012), Article ID 376546, 26 pages

http://dx.doi.org/10.1155/2012/376546

Research Article

## Predictor-Corrector Primal-Dual Interior Point Method for Solving Economic Dispatch Problems: A Postoptimization Analysis

^{1}Department of Mathematics, Universidade Estadual Paulista (UNESP), 17033-360 Bauru, SP, Brazil^{2}Graduate Program in Electrical Engineering, Universidade Estadual Paulista (UNESP), 17033-360 Bauru, SP, Brazil^{3}Department 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.

#### Linked References

- N. Karmarkar, “A new polynomial-time algorithm for linear programming,”
*Combinatorica*, vol. 4, no. 4, pp. 373–395, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - I. I. Dikin, “Iterative solution of problems of linear and quadratic programming,”
*Doklady Akademii Nauk SSSR*, vol. 174, pp. 747–748, 1967 (Russian). View at Zentralblatt MATH - E. R. Barnes, “A variation on Karmarkar's algorithm for solving linear programming problems,”
*Mathematical Programming*, vol. 36, no. 2, pp. 174–182, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - 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. View at Publisher · View at Google Scholar · View at Scopus - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - Y. Ye, “An $O({n}^{3}L)$ potential reduction algorithm for linear programming,” in
*Contemporary Mathematics*, vol. 114, pp. 91–107, American Mathematical Society, Providence, RI, USA, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - J. Renegar, “A polynomial-time algorithm, based on Newton's method, for linear programming,”
*Mathematical Programming*, vol. 40, no. 1, pp. 59–93, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - P. M. Vaidya, “An algorithm for linear programming which requires $O(((m+n){n}^{2}+{(m+n)}^{1.5}n)L)$ arithmetic operations,”
*Mathematical Programming*, vol. 47, no. 2, pp. 175–201, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - 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. View at Zentralblatt MATH - C. C. Gonzaga, “An algorithm for solving linear programming problems in $O({n}^{3}L)$ operations,” in
*Progress in Mathematical Programming: Interior-Point and Related Methods*, N. Megiddo, Ed., pp. 1–28, Springer, New York, NY, USA, 1989. View at Zentralblatt MATH - C. C. Gonzaga, “Polynomial affine algorithms for linear programming,”
*Mathematical Programming*, vol. 49, no. 1, pp. 7–21, 1990. View at Publisher · View at Google Scholar - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - 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. View at Zentralblatt MATH - S. Mehrotra and J. Sun, “An algorithm for convex quadratic programming that requires $O({n}^{3.5}L)$ arithmetic operations,”
*Mathematics of Operations Research*, vol. 15, no. 2, pp. 342–363, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - 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. View at Publisher · View at Google Scholar · View at Scopus - 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. View at Publisher · View at Google Scholar · View at Scopus - 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. View at Scopus - 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. View at Publisher · View at Google Scholar · View at Scopus - 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.