IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v68y2017i1d10.1007_s10898-016-0451-3.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-016-0451-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-016-0451-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    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. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. O’Brien, Thomas & Reeb, Tyler, 2016. "Freight Efficiency Strategies: Operational Modernization at Distribution Nodes," Institute of Transportation Studies, Working Paper Series qt4fg9f0gv, Institute of Transportation Studies, UC Davis.
    8. Li, Han-Lin & Fang, Shu-Cherng & Huang, Yao-Huei & Nie, Tiantian, 2016. "An enhanced logarithmic method for signomial programming with discrete variables," European Journal of Operational Research, Elsevier, vol. 255(3), pages 922-934.
    9. 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.
    10. Consiglio, Andrea & Carollo, Angelo & Zenios, Stavros A., 2014. "Generating Multi-factor Arbitrage-Free Scenario Trees with Global Optimization," Working Papers 13-35, University of Pennsylvania, Wharton School, Weiss Center.
    11. Scott J. Davis & Shatiel B. Edwards & Gerald E. Teper & David G. Bassett & Michael J. McCarthy & Scott C. Johnson & Craig R. Lawton & Matthew J. Hoffman & Liliana Shelton & Stephen M. Henry & Darryl J, 2016. "Maximizing the U.S. Army’s Future Contribution to Global Security Using the Capability Portfolio Analysis Tool (CPAT)," Interfaces, INFORMS, vol. 46(1), pages 91-108, February.
    12. Joey Huchette & Joey Huchette, 2019. "A Combinatorial Approach for Small and Strong Formulations of Disjunctive Constraints," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 793-820, August.
    13. Xinlei Wang & Johan Lim & Seung-Jean Kim & Kyu Hahn, 2015. "Estimating cell probabilities in contingency tables with constraints on marginals/conditionals by geometric programming with applications," Computational Statistics, Springer, vol. 30(1), pages 107-129, March.
    14. Angelo Ciccazzo & Vittorio Latorre & Giampaolo Liuzzi & Stefano Lucidi & Francesco Rinaldi, 2015. "Derivative-Free Robust Optimization for Circuit Design," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 842-861, March.
    15. Liu, Haoxiang & Wang, David Z.W., 2015. "Global optimization method for network design problem with stochastic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 72(C), pages 20-39.
    16. Amir Ardestani-Jaafari & Erick Delage, 2016. "Robust Optimization of Sums of Piecewise Linear Functions with Application to Inventory Problems," Operations Research, INFORMS, vol. 64(2), pages 474-494, April.
    17. Fang Yang & Yao-Huei Huang, 2021. "An optimization approach for winner determination problem considering transportation cost discounts," Journal of Global Optimization, Springer, vol. 80(3), pages 711-728, July.
    18. Lu, Yiping & Chen, Danny Z., 2021. "A new exact algorithm for the Weapon-Target Assignment problem," Omega, Elsevier, vol. 98(C).
    19. M. Hosein Zare & Juan S. Borrero & Bo Zeng & Oleg A. Prokopyev, 2019. "A note on linearized reformulations for a class of bilevel linear integer problems," Annals of Operations Research, Springer, vol. 272(1), pages 99-117, January.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:68:y:2017:i:1:d:10.1007_s10898-016-0451-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.