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Global Optimization of Linear Multiplicative Programming Using Univariate Search

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Fuzzy Information & Engineering and Operations Research & Management

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 211))

Abstract

We show that, by using suitable transformations and introducing auxiliary variables, linear multiplicative program can be converted into an equivalent parametric convex programming problem, parametric concave minimization problem or parametric D.C. programming. Then potential and known methods for globally solving linear multiplicative program become available.

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References

  1. Matsui, T.: NP-Hardness of Linear Multiplicative Programming and Related Problems. J. of Global Optimization. 9, 113–119 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  2. Maranas, C.D., Androulakis, I.P., Floudas, C.A., Berger, A.J., Mulvey, J.M.: Solving long-term financial planning problems via global optimization. Journal of Economic Dynamics and Control. 21, 1405–1425 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  3. Quesada I., Grossmann I.E.: Alternative bounding approximations for the global optimization of various engineering design problems, in: I.E. Grossmann (Ed.), Global Optimization in Engineering Design, Nonconvex Optimization and Its Applications, Vol. 9, Kluwer Academic Publishers, Norwell, MA,pp. 309–331 (1996).

    Google Scholar 

  4. Mulvey, J.M., Vanderbei, R.J., Zenios, S.A.: Robust optimization of large-scale systems. Operations Research. 43, 264–281 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  5. Dorneich, M.C., Sahinidis, N.V.: Global optimization algorithms for chip design and compaction. Engineering Optimization. 25(2), 131–154 (1995)

    Article  Google Scholar 

  6. Bennett, K.P., Mangasarian, O.L.: Bilinear separation of two sets in n-space. Computational Optimization and Applications. 2, 207–227 (1994)

    Article  MathSciNet  Google Scholar 

  7. Konno, H., Kuno, T., Yajima, Y.: Global optimization of a generalized convex multiplicative function. Journal of Global Optimization. 4, 47–62 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  8. Benson, H.P.: An outcome space branch and bound-outer approximation algorithm for convex multiplicative programming. Journal of Global Optimization. 15, 315–342 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhou, X.G., Wu, K.: A accelerating method for a class of multiplicative programming with exponent. Journal of Computational and Applied Mathematics 223, 975–982 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Bennett, K.P.: Global tree optimization: a non-greedy decision tree algorithm. Computing Sciences and Statistics. 26, 156–160 (1994)

    Google Scholar 

  11. Falk, J.E., Palocsa, S.W.: Image space analysis of generalized fractional programs. Journal of Global Optimization. 4(1), 63–88 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  12. Benson, H.P., Boger, G.M.: Outcome-space cutting-plane algorithm for linear multiplicative programming. Journal of Optimization Theory and Applications. 104(2), 301–322 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  13. Benson, H.P., Boger, G.M.: Multiplicative programming problems: analysis and efficient point search heuristic. Journal of Optimization Theory and Applications. 94(2), 487–510 (1997)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

Thanks to the support by National Natural Science Foundation of China (No.70771030 and No.70271047) and Project Science Foundation of Guangdong University of Finance(No.11XJ02-12 and No.2012RCYJ005).

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Authors and Affiliations

  1. Department of Applied Mathematics, Guangdong University of Finance, Guangzhou, 510521, Guangzhou, China

    Xue-gang Zhou

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  1. Xue-gang Zhou
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Correspondence to Xue-gang Zhou .

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Editors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University Higher Education Mega Center, Guangzhou, People's Republic of China

    Bing-Yuan Cao

  2. Department of Mathematics and Computer Sciences, Mazandaran University, Babolsar, Iran

    Hadi Nasseri

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Zhou, Xg. (2014). Global Optimization of Linear Multiplicative Programming Using Univariate Search. In: Cao, BY., Nasseri, H. (eds) Fuzzy Information & Engineering and Operations Research & Management. Advances in Intelligent Systems and Computing, vol 211. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38667-1_6

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  • DOI: https://doi.org/10.1007/978-3-642-38667-1_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38666-4

  • Online ISBN: 978-3-642-38667-1

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