Global optimization of generalized geometric programming
Global optimization of generalized geometric programming
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DOI：
10.1016/j.camwa.2004.07.008
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发表时间：
2004-11
影响因子：
2.9
通讯作者：
Yanjun Wang;Kecun Zhang;Yuelin Gao
中科院分区：
文献类型：
--
作者：
Yanjun Wang;Kecun Zhang;Yuelin Gao
本文提出了一种确定性全局优化算法，用于求解广义几何规划（GGP）问题的全局最小值。利用指数变量变换等技巧，将初始非凸问题（GGP）转化为一个典型的反凸规划（RCP）。然后利用著名的算术-几何平均不等式和超矩形区域内反向约束的线性上界，得到了问题的线性松弛（RCP）。通过对目标函数可行域的线性松弛和一系列线性优化问题的求解，证明了所提出的分支定界算法收敛于全局最小值.最后通过数值实验验证了算法的可行性和鲁棒稳定性。
In this paper a deterministic global optimization algorithm is proposed for locatingthe global minimum of the generalized geometric programming (GGP) problem. By utilizing an exponential variable transformation and some other techniques the initial nonconvex problem (GGP) is reduced to a typical reverse convex programming (RCP). Then a linear relaxation of problem (RCP) is obtained based on the famous arithmetic-geometric mean inequality and the linear upper bound of the reverse constraints inside some hyperrectangle region. The proposed branch and bound algorithm is convergent to the global minimum through the successive refinement of the linear relaxation of the feasible region of the objective function and the solutions of a series of linear optimization problems. And finally the numerical experiment is given to illustrate the feasibility and the robust stability of the present algorithm.