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An accelerated extended cutting plane approach with piecewise linear approximations for signomial geometric programming

Author

Listed:
  • Yiduo Zhan

    (University of Central Florida)

  • Qipeng P. Zheng

    (University of Central Florida)

  • Chung-Li Tseng

    (UNSW)

  • Eduardo L. Pasiliao

    (Air Force Research Laboratory)

Abstract

This paper presents a global optimization approach for solving signomial geometric programming (SGP) problems. We employ an accelerated extended cutting plane (ECP) approach integrated with piecewise linear (PWL) approximations to solve the global optimization of SGP problems. In this approach, we separate the feasible regions determined by the constraints into convex and nonconvex ones in the logarithmic domain. In the nonconvex feasible regions, the corresponding constraint functions are converted into mixed integer linear constraints using PWL approximations, while the other constraints with convex feasible regions are handled by the ECP method. We also use pre-processed initial cuts and batched cuts to accelerate the proposed algorithm. Numerical results show that the proposed approach can solve the global optimization of SGP problems efficiently and effectively.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:70:y:2018:i:3:d:10.1007_s10898-017-0563-4
    DOI: 10.1007/s10898-017-0563-4
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    References listed on IDEAS

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    1. Mandal, Nirmal Kumar & Roy, Tapan Kumar & Maiti, Manoranjan, 2006. "Inventory model of deteriorated items with a constraint: A geometric programming approach," European Journal of Operational Research, Elsevier, vol. 173(1), pages 199-210, August.
    2. 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.
    3. Xu, Gongxian, 2014. "Global optimization of signomial geometric programming problems," European Journal of Operational Research, Elsevier, vol. 233(3), pages 500-510.
    4. 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.
    5. Tsai, Jung-Fa & Lin, Ming-Hua & Hu, Yi-Chung, 2007. "On generalized geometric programming problems with non-positive variables," European Journal of Operational Research, Elsevier, vol. 178(1), pages 10-19, April.
    6. Richard J. Clasen, 1984. "The Solution of the Chemical Equilibrium Programming Problem with Generalized Benders Decomposition," Operations Research, INFORMS, vol. 32(1), pages 70-79, February.
    7. 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.
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    Cited by:

    1. Rashed Khanjani-Shiraz & Salman Khodayifar & Panos M. Pardalos, 2021. "Copula theory approach to stochastic geometric programming," Journal of Global Optimization, Springer, vol. 81(2), pages 435-468, October.

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