Journal of Global Optimization

, Volume 56, Issue 3, pp 1123–1142

Branch-reduction-bound algorithm for generalized geometric programming

Authors

    • College of Mathematics and Information ScienceHenan Normal University
  • Xiaoai Li
    • College of Mathematics and Information ScienceHenan Normal University
Article

DOI: 10.1007/s10898-012-9933-0

Cite this article as:
Shen, P. & Li, X. J Glob Optim (2013) 56: 1123. doi:10.1007/s10898-012-9933-0

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.

Keywords

Generalized geometric programmingGlobal optimizationMonotonic functionReduction operation
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Copyright information

© Springer Science+Business Media, LLC. 2012