About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 163263, 12 pages
http://dx.doi.org/10.1155/2014/163263
Research Article

A Global Optimization Algorithm for Signomial Geometric Programming Problem

College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China

Received 17 December 2013; Accepted 16 January 2014; Published 30 March 2014

Academic Editor: Yisheng Song

Copyright © 2014 Xue-Ping Hou 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

  1. P. Hansen and B. Jaumard, “Reduction of indefinite quadratic programs to bilinear programs,” Journal of Global Optimization, vol. 2, no. 1, pp. 41–60, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. C. S. Beightler and D. T. Phillips, Applied Geometric Programming, John Wiley & Sons, New York, NY, USA, 1976. View at MathSciNet
  3. M. Avriel and A. C. Williams, “An extension of geometric programming with applications in engineering optimization,” Journal of Engineering Mathematics, vol. 5, no. 2, pp. 187–194, 1971. View at Publisher · View at Google Scholar · View at Scopus
  4. N. K. Jha, “Geometric programming based robot control design,” Computers and Industrial Engineering, vol. 29, no. 1–4, pp. 631–635, 1995. View at Scopus
  5. T. R. Jefferson and C. H. Scott, “Generalized geometric programming applied to problems of optimal control. I. Theory,” Journal of Optimization Theory and Applications, vol. 26, no. 1, pp. 117–129, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. J. G. Ecker, “Geometric programming: methods, computations and applications,” SIAM Review, vol. 22, no. 3, pp. 338–362, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. R. Horst and H. Tuy, Global Optimization: Deterministic Approaches, Springer, Berlin, Germany, 2nd edition, 1993. View at MathSciNet
  8. C. A. Floudas and V. Visweswaran, “Quadratic optimization,” in Handbook of Global Optimization, Nonconvex Optimization and Its Applications, R. Horst and P. M. Pardalos, Eds., vol. 2, pp. 217–269, Kluwer Academic Publishers, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Y. K. Sui, “The expansion of functions under transformation and its application to optimization,” Computer Methods in Applied Mechanics and Engineering, vol. 113, no. 3-4, pp. 253–262, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. K. Das, T. K. Roy, and M. Maiti, “Multi-item inventory model with quantity-dependent inventory costs and demand-dependent unit cost under imprecise objective and restrictions: a geometric programming approach,” Production Planning and Control, vol. 11, no. 8, pp. 781–788, 2000. View at Publisher · View at Google Scholar · View at Scopus
  11. R. J. Duffin and E. L. Peterson, “Duality theory for geometric programming,” SIAM Journal on Applied Mathematics, vol. 14, pp. 1307–1349, 1966. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. R. J. Duffin, E. L. Peterson, and C. Zener, “The geometric inequality and the main lemma,” in Geometric Programming Theory and Applocations, pp. 115–140, John Wiley & Sons, New York, NY, USA, 1967.
  13. R. J. Duffin and E. L. Peterson, “Geometric programming with signomials,” Journal of Optimization Theory and Applications, vol. 11, pp. 3–35, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. U. Passy, “Generalized weighted mean programming,” SIAM Journal on Applied Mathematics, vol. 20, pp. 763–778, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. U. Passy and D. J. Wilde, “Generalized polynomial optimization,” SIAM Journal on Applied Mathematics, vol. 15, pp. 1344–1356, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. K. O. Kortanek, X. Xu, and Y. Ye, “An infeasible interior-point algorithm for solving primal and dual geometric programs,” Mathematical Programming, vol. 76, no. 1, pp. 155–181, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. H. D. Sherali and C. H. Tuncbilek, “A global optimization algorithm for polynomial programming problems using a reformulation-linearization technique,” Journal of Global Optimization, vol. 2, no. 1, pp. 101–112, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. H. D. Sherali and C. H. Tuncbilek, “A reformulation-convexification approach for solving nonconvex quadratic programming problems,” Journal of Global Optimization, vol. 7, no. 1, pp. 1–31, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. H. D. Sherali, “Global optimization of nonconvex polynomial programming problems having rational exponents,” Journal of Global Optimization, vol. 12, no. 3, pp. 267–283, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. C. D. Maranas and C. A. Floudas, “Global optimization in generalized geometric programming,” Computers and Chemical Engineering, vol. 21, no. 4, pp. 351–369, 1997. View at Scopus
  21. P. P. Shen and K. C. Zhang, “Global optimization of signomial geometric programming using linear relaxation,” Applied Mathematics and Computation, vol. 150, no. 1, pp. 99–114, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. P. P. Shen, Y. Ma, and Y. Q. Chen, “A robust algorithm for generalized geometric programming,” Journal of Global Optimization, vol. 41, no. 4, pp. 593–612, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. Y. J. Wang, T. Li, and Z. A. Liang, “A general algorithm for solving generalized geometric programming with nonpositive degree of difficulty,” Computational Optimization and Applications, vol. 44, no. 1, pp. 139–158, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. S. J. Qu, K. C. Zhang, and F. S. Wang, “A global optimization using linear relaxation for generalized geometric programming,” European Journal of Operational Research, vol. 190, no. 2, pp. 345–356, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. H. Tuy, “Effect of the subdivision strategy on convergence and efficiency of some global optimization algorithms,” Journal of Global Optimization, vol. 1, no. 1, pp. 23–36, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. J.-M. Peng and Y.-X. Yuan, “Optimality conditions for the minimization of a quadratic with two quadratic constraints,” SIAM Journal on Optimization, vol. 7, no. 3, pp. 579–594, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. P. P. Shen, X. D. Bai, and W. M. Li, “A new accelerating method for globally solving a class of nonconvex programming problems,” Nonlinear Analysis. Theory, Methods & Applications, vol. 71, no. 7-8, pp. 2866–2876, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. R. Horst, P. M. Pardalos, and N. V. Thoai, Introduction to Global Optimization, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000. View at MathSciNet
  29. R. Horst and H. Tuy, Global Optimization: Deterministic Approaches, Springer, Berlin, Germany, 3rd edition, 2003. View at MathSciNet
  30. R. Horst, “Deterministic global optimization with partition sets whose feasibility is not known: application to concave minimization, reverse convex constraints, DC-programming, and Lipschitzian optimization,” Journal of Optimization Theory and Applications, vol. 58, no. 1, pp. 11–37, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  31. S.-J. Qu, K.-C. Zhang, and Y. Ji, “A new global optimization algorithm for signomial geometric programming via Lagrangian relaxation,” Applied Mathematics and Computation, vol. 184, no. 2, pp. 886–894, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. Y. J. Wang and Z. A. Liang, “A deterministic global optimization algorithm for generalized geometric programming,” Applied Mathematics and Computation, vol. 168, no. 1, pp. 722–737, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. P. P. Shen and H. W. Jiao, “A new rectangle branch-and-pruning approach for generalized geometric programming,” Applied Mathematics and Computation, vol. 183, no. 2, pp. 1027–1038, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  34. M. J. Rijckaert and X. M. Martens, “Comparison of generalized geometric programming algorithms,” Journal of Optimization Theory and Application, vol. 26, pp. 205–241, 1978.