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Improved logarithmic linearizing method for optimization problems with free-sign pure discrete signomial terms

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  • Hao-Chun Lu

    (Fu Jen Catholic University)

Abstract

Free-sign pure discrete signomial (FPDS) terms are vital to and are frequently observed in many nonlinear programming problems, such as geometric programming, generalized geometric programming, and mixed-integer non-linear programming problems. In this study, all variables in the FPDS term are discrete variables. Any improvement to techniques for linearizing FPDS term contributes significantly to the solving of nonlinear programming problems; therefore, relative techniques have continually been developed. This study develops an improved exact method to linearize a FPDS term into a set of linear programs with minimal logarithmic numbers of zero-one variables and constraints. This method is tighter than current methods. Various numerical experiments demonstrate that the proposed method is significantly more efficient than current methods, especially when the problem scale is large.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:68:y:2017:i:1:d:10.1007_s10898-016-0451-3
    DOI: 10.1007/s10898-016-0451-3
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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. 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. 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.
    4. 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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