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Global Optimization for Generalized Geometric Programs with Mixed Free-Sign Variables

Author

Listed:
  • Han-Lin Li

    (Institute of Information Management, National Chiao Tung University, Taiwan, Republic of China)

  • Hao-Chun Lu

    (Institute of Information Management, National Chiao Tung University, Taiwan, Republic of China)

Abstract

Many optimization problems are formulated as generalized geometric programming (GGP) containing signomial terms f ( X )· g ( Y ), where X and Y are continuous and discrete free-sign vectors, respectively. By effectively convexifying f ( X ) and linearizing g ( Y ), this study globally solves a GGP with a lower number of binary variables than are used in current GGP methods. Numerical experiments demonstrate the computational efficiency of the proposed method.

Suggested Citation

  • Han-Lin Li & Hao-Chun Lu, 2009. "Global Optimization for Generalized Geometric Programs with Mixed Free-Sign Variables," Operations Research, INFORMS, vol. 57(3), pages 701-713, June.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:3:p:701-713
    DOI: 10.1287/opre.1080.0586
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    References listed on IDEAS

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    1. Han-Lin Li, 1999. "Incorporating Competence Sets of Decision Makers by Deduction Graphs," Operations Research, INFORMS, vol. 47(2), pages 209-220, April.
    2. Stephen P. Boyd & Seung-Jean Kim & Dinesh D. Patil & Mark A. Horowitz, 2005. "Digital Circuit Optimization via Geometric Programming," Operations Research, INFORMS, vol. 53(6), pages 899-932, December.
    3. Hao Cheng & Shu-Cherng Fang & John Lavery, 2005. "A Geometric Programming Framework for Univariate Cubic L 1 Smoothing Splines," Annals of Operations Research, Springer, vol. 133(1), pages 229-248, January.
    4. Ecker, J.G. & Wiebking, R.D., 1978. "Optimal design of a dry-type natural-draft cooling tower by geometric programming," LIDAM Reprints CORE 355, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

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    3. Lu, Hao-Chun, 2020. "Indicator of power convex and exponential transformations for solving nonlinear problems containing posynomial terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    4. Xu, Gongxian, 2014. "Global optimization of signomial geometric programming problems," European Journal of Operational Research, Elsevier, vol. 233(3), pages 500-510.
    5. Tseng, Chung-Li & Zhan, Yiduo & Zheng, Qipeng P. & Kumar, Manish, 2015. "A MILP formulation for generalized geometric programming using piecewise-linear approximations," European Journal of Operational Research, Elsevier, vol. 245(2), pages 360-370.
    6. Hao-Chun Lu & Liming Yao, 2019. "Efficient Convexification Strategy for Generalized Geometric Programming Problems," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 226-234, April.
    7. Qi An & Shu-Cherng Fang & Tiantian Nie & Shan Jiang, 2018. "$$\ell _1$$ ℓ 1 -Norm Based Central Point Analysis for Asymmetric Radial Data," Annals of Data Science, Springer, vol. 5(3), pages 469-486, September.
    8. Lin, Ming-Hua & Tsai, Jung-Fa, 2012. "Range reduction techniques for improving computational efficiency in global optimization of signomial geometric programming problems," European Journal of Operational Research, Elsevier, vol. 216(1), pages 17-25.
    9. Yang, Fang & Huang, Yao-Huei, 2020. "Linearization technique with superior expressions for centralized planning problem with discount policy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    10. Warren P. Adams & Stephen M. Henry, 2012. "Base-2 Expansions for Linearizing Products of Functions of Discrete Variables," Operations Research, INFORMS, vol. 60(6), pages 1477-1490, December.
    11. Hao-Chun Lu, 2017. "Improved logarithmic linearizing method for optimization problems with free-sign pure discrete signomial terms," Journal of Global Optimization, Springer, vol. 68(1), pages 95-123, May.
    12. Yiduo Zhan & Qipeng P. Zheng & Chung-Li Tseng & Eduardo L. Pasiliao, 2018. "An accelerated extended cutting plane approach with piecewise linear approximations for signomial geometric programming," Journal of Global Optimization, Springer, vol. 70(3), pages 579-599, March.
    13. Han-Lin Li & Yao-Huei Huang & Shu-Cherng Fang, 2017. "Linear Reformulation of Polynomial Discrete Programming for Fast Computation," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 108-122, February.
    14. Han-Lin Li & Yao-Huei Huang & Shu-Cherng Fang, 2013. "A Logarithmic Method for Reducing Binary Variables and Inequality Constraints in Solving Task Assignment Problems," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 643-653, November.
    15. Zejian Qin & Bingyuan Cao & Shu-Cherng Fang & Xiao-Peng Yang, 2018. "Geometric Programming with Discrete Variables Subject to Max-Product Fuzzy Relation Constraints," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-8, April.
    16. Fukasawa, Ricardo & Naoum-Sawaya, Joe & Oliveira, Daniel, 2024. "The price-elastic knapsack problem," Omega, Elsevier, vol. 124(C).

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