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Indicator of power convex and exponential transformations for solving nonlinear problems containing posynomial terms

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  • Lu, Hao-Chun

Abstract

Posynomial terms frequently appear in many nonlinear problems and are the core components of geometric and generalized geometric programming problems. The most popular method to treat nonconvex posynomial terms for obtaining global optimization is to convert nonconvex posynomial terms as convex underestimators using transformation techniques. Among the transformation techniques, exponential transformation (ET) and power convex transformation (PCT) can yield the tightest underestimators of posynomial terms. However, the current literature has rarely discussed which to select between ET and PCT. This study employs the definite integral with piecewise linear technique to calculate the error between the original posynomial and the corresponding ET/PCT underestimators. Lastly, this study aims to identify an indicator that can choose the appropriate transformation between ET and PCT and analyze the correctness of the proposed indicator for posynomial terms in nonlinear problems. The proposed indicator can efficiently solve nonlinear problems containing posynomial terms. Numerical examples are used to demonstrate the efficacy of the proposed indicator.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:538:y:2020:i:c:s0378437119315171
    DOI: 10.1016/j.physa.2019.122658
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    References listed on IDEAS

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    1. 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.
    2. Hao-Chun Lu & Han-Lin Li & Chrysanthos Gounaris & Christodoulos Floudas, 2010. "Convex relaxation for solving posynomial programs," Journal of Global Optimization, Springer, vol. 46(1), pages 147-154, January.
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    4. 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.
    5. Jung-Fa Tsai & Ming-Hua Lin, 2011. "An Efficient Global Approach for Posynomial Geometric Programming Problems," INFORMS Journal on Computing, INFORMS, vol. 23(3), pages 483-492, August.
    6. 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.
    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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