| 广义几何规划的全局优化算法 |
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| 引用本文： | 申培萍,杨长森. 广义几何规划的全局优化算法[J]. 数学物理学报(A辑), 2006, 26(3): 382-386 |
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| 作者姓名： | 申培萍 杨长森 |
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| 作者单位： | 河南师范大学数学与信息科学学院，河南师范大学数学与信息科学学院 新乡 453007，新乡 453007 |
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| 基金项目： | 河南省自然科学基金(0511011500)河南省软科学研究计划(0513030920)河南省教育厅自然科学基金(2004110007)资助 |
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| 摘 要： | 对许多工程设计中常用的广义几何规划问题(GGP)提出一种确定性全局优化算法,该算法利用目标和约束函数的线性下界估计,建立GGP的松弛线性规划(RLP),从而将原来非凸问题(GGP)的求解过程转化为求解一系列线性规划问题(RLP).通过可行域的连续细分以及一系列线性规划的解,提出的分枝定界算法收敛到GGP的全局最优解,且数值例子表明了算法的可行性.
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| 关 键 词： | 广义几何规划 线性化方法 全局优化 |
| 文章编号： | 1003-3998(2006)03-382-05 |
| 收稿时间： | 2004-09-18 |
| 修稿时间： | 2005-08-08 |
Algorithm of Global Optimization for Generalized Geometric Programming |
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| Shen Peiping,Yang Changsen. Algorithm of Global Optimization for Generalized Geometric Programming[J]. Acta Mathematica Scientia, 2006, 26(3): 382-386 |
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| Authors: | Shen Peiping Yang Changsen |
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| Affiliation: | College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007 |
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| Abstract: | A deterministic global optimization algorithm is proposed for locating global minimum of generalized geometric programming (GGP), which can be applied to engineering designs. By utilizing the linear underestimates of the objective and constraint functions, the relaxation linear programming (RLP) about GGP is established, thus the initial non-convex problem (GGP) is reduced to a series of linear programming (RLP).The proposed branch and bound algorithm is convergent to the global minimum of GGP through the successive refinement of the feasible region and the solutions of a series of RLP. And finally the numerical example is given to illustrate the feasibility of the present algorithm. |
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| Keywords: | Generalized geometric programming Linearization method Global optimization. |
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