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Global optimization method for linear multiplicative programming

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Abstract

In this paper, a new global algorithm is presented to globally solve the linear multiplicative programming (LMP). The problem (LMP) is firstly converted into an equivalent programming problem (LMP (H)) by introducing p auxiliary variables. Then by exploiting structure of (LMP(H)), a linear relaxation programming (LP (H)) of (LMP (H)) is obtained with a problem (LMP) reduced to a sequence of linear programming problems. The algorithm is used to compute the lower bounds called the branch and bound search by solving linear relaxation programming problems (LP(H)). The proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong, Higher Education Institutes, Guangzhou University, Guangzhou, 510006, China

    Xue-gang Zhou & Bing-yuan Cao

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

    Xue-gang Zhou

  3. School of Mathematical Science and Computing Technology, Center South University, Changsha, 410075, China

    Kun Wu

Authors
  1. Xue-gang Zhou
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  2. Bing-yuan Cao
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  3. Kun Wu
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Corresponding author

Correspondence to Bing-yuan Cao.

Additional information

Supported by the PhD Start-up Fund of Natural Science Foundation of Guangdong Province, China (No. S2013040012506) and China Postdoctoral Science Foundation Funded Project (2014M562152).

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Zhou, Xg., Cao, By. & Wu, K. Global optimization method for linear multiplicative programming. Acta Math. Appl. Sin. Engl. Ser. 31, 325–334 (2015). https://doi.org/10.1007/s10255-015-0456-6

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  • DOI: https://doi.org/10.1007/s10255-015-0456-6

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