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

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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.

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Acknowledgments

This research is supported by the National Science Council of Taiwan under grants NSC 102-2410-H-030-063-MY3. The authors wish to thank the area editor, the associate editor, and the anonymous referees for providing insightful comments and suggestions, which have helped me improve the quality of the paper.

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  1. Department of Information Management, College of Management, Fu Jen Catholic University, No. 510, Jhongjheng Rd., Sinjhuang City, 242, Taipei County, Taiwan

    Hao-Chun Lu

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Lu, HC. Improved logarithmic linearizing method for optimization problems with free-sign pure discrete signomial terms. J Glob Optim 68, 95–123 (2017). https://doi.org/10.1007/s10898-016-0451-3

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