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Branch-reduction-bound algorithm for generalized geometric programming

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Abstract

This article presents a branch-reduction-bound algorithm for globally solving the generalized geometric programming problem. To solve the problem, an equivalent monotonic optimization problem whose objective function is just a simple univariate is proposed by exploiting the particularity of this problem. In contrast to usual branch-and-bound methods, in the algorithm the upper bound of the subproblem in each node is calculated easily by arithmetic expressions. Also, a reduction operation is introduced to reduce the growth of the branching tree during the algorithm search. The proposed algorithm is proven to be convergent and guarantees to find an approximative solution that is close to the actual optimal solution. Finally, numerical examples are given to illustrate the feasibility and efficiency of the present algorithm.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, People’s Republic of China

    Peiping Shen & Xiaoai Li

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  1. Peiping Shen
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  2. Xiaoai Li
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Correspondence to Peiping Shen.

Additional information

Research supported by NSFC (11171094; 11171368) and Innovation Scientists and Technicians Troop Construction Projects of Henan Province (114200510011).

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Shen, P., Li, X. Branch-reduction-bound algorithm for generalized geometric programming. J Glob Optim 56, 1123–1142 (2013). https://doi.org/10.1007/s10898-012-9933-0

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  • DOI: https://doi.org/10.1007/s10898-012-9933-0

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