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A robust algorithm for generalized geometric programming

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Abstract

Most existing methods of global optimization for generalized geometric programming (GGP) actually compute an approximate optimal solution of a linear or convex relaxation of the original problem. However, these approaches may sometimes provide an infeasible solution, or far from the true optimum. To overcome these limitations, a robust solution algorithm is proposed for global optimization of (GGP) problem. This algorithm guarantees adequately to obtain a robust optimal solution, which is feasible and close to the actual optimal solution, and is also stable under small perturbations of the constraints.

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References

  1. Avriel M. and Williams A.C. (1971). An extension of geometric programming with applications in engineering optimization. J. Eng. Math. 5(3): 187–199

    Article  Google Scholar 

  2. Jefferson T.R. and Scott C.H. (1978). Generalized geometric programming applied to problems of optimal control: I. Theory. J. Optim. Theory Appl. 26: 117–129

    Article  Google Scholar 

  3. Nand K.J. (1995). Geometric programming based robot control design. Comput. Indust. Eng. 29(1–4): 631–635

    Google Scholar 

  4. Das K., Roy T.K. and Maiti M. (2000). Multi-item inventory model with under imprecise objective and restrictions: a geometric programming approach. Production Plan. Control 11(8): 781–788

    Article  Google Scholar 

  5. Jae Chul C. and Bricker Dennis L. (1996). Effectiveness of a geometric programming algorithm for optimization of machining economics models. Comput. Oper. Res. 23(10): 957–961

    Article  Google Scholar 

  6. EI Barmi H. and Dykstra R.L. (1994). Restricted multinomial maximum likelihood estimation based upon Fenchel duality. Stat. Probab. Lett. 21: 121–130

    Article  Google Scholar 

  7. Bricker D.L., Kortanek K.O. and Xu L. (1995). Maximum Likelihood Estimates with Order Restrictions on Probabilities and Odds Ratios: A Geometric Programming Approach. Applied Mathematical and Computational Sciences, the University of IA, Iowa City, IA

  8. Jagannathan R. (1990). A stochastic geometric programming problem with multiplicative recourse. Oper. Res. Lett. 9: 99–104

    Article  Google Scholar 

  9. Sönmez A.I., Baykasoglu A., Dereli T. and Filiz I.H. (1999). Dynamic optimization of multipass milling operations via geometric programming. Int. J. Machine Tools Manuf. 39: 297–320

    Article  Google Scholar 

  10. Scott C.H. and Jefferson T.R. (1995). Allocation of resources in project management. Int. J. Syst. Sci. 26: 413–420

    Article  Google Scholar 

  11. Maranas C.D. and Floudas C.A. (1997). Global optimization in generalized geometric programming. Comput. Chem. Eng. 21(4): 351–369

    Article  Google Scholar 

  12. Rijckaert M.J. and Martens X.M. (1974). Analysis and optimization of the Williams-Otto process by geometric programming. AICHE J 20(4): 742–750

    Article  Google Scholar 

  13. Shen P. and Zhang K. (2004). Global optimization of signomial geometric programming using linear relaxation. Appl. Math. Comput. 150: 99–114

    Article  Google Scholar 

  14. Wang Y., Zhang K. and Gao Y. (2004). Global optimization of generalized geometric programming. Comput. Math. Appl. 48: 1505–1516

    Article  Google Scholar 

  15. Tuy H. (2005). Robust solution of nonconvex global optimization problems. J. Glob. Optim. 32: 357–374

    Google Scholar 

  16. Tuy H. (2000). Monotonic optimization: problems and solution approaches. SIAM J. Optim. 11(2): 464–494

    Article  Google Scholar 

  17. Tuy H., Al-Khayyal F. and Thach P.T. (2005). Monotonic optimization: branch and cut methods. In: Audet, C., Hansen, P., and Savard, G. (eds) Essays and Surveys on Global Optimization, pp 39–38. Springer, Berlin

    Chapter  Google Scholar 

  18. Qu S.-J., Zhang K.-C. and Ji Y. (2007). A new global optimization algorithm for signomial geometric programming via Lagrangian relaxation. Appl. Math. Comput. 184(2): 886–894

    Article  Google Scholar 

  19. Wang Y. and Liang Z. (2005). A deterministic global optimization algorithm for generalized geometric programming. Appl. Math. Comput. 168: 722–737

    Article  Google Scholar 

  20. Shen P. and Jiao H. (2006). A new rectangle branch-and-pruning approach for generalized geometric programming. Appl. Math. Comput. 183: 1027–1038

    Article  Google Scholar 

  21. Tuy H. (2005). Polynomial optimization: a robust approach. Pacific J. Optim. 1: 357–374

    Google Scholar 

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Authors and Affiliations

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, P.R.China

    Peiping Shen, Yuan Ma & Yongqiang Chen

Authors
  1. Peiping Shen
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  2. Yuan Ma
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  3. Yongqiang Chen
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Correspondence to Peiping Shen.

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Shen, P., Ma, Y. & Chen, Y. A robust algorithm for generalized geometric programming. J Glob Optim 41, 593–612 (2008). https://doi.org/10.1007/s10898-008-9283-0

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  • DOI: https://doi.org/10.1007/s10898-008-9283-0

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