| 带自由变量的广义几何规划全局求解的新算法 |
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| 引用本文： | 靳利,刘慧芳,裴永刚.带自由变量的广义几何规划全局求解的新算法[J].数学的实践与认识,2012,42(12):100-106. |
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| 作者姓名： | 靳利 刘慧芳 裴永刚 |
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| 作者单位： | 1. 河南机电高等专科学校基础部,河南新乡,453003
2. 河南师范大学数学与信息科学学院,河南新乡,450001 |
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| 基金项目： | 河南省教育厅自然科学研究计划项目 |
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| 摘 要： | 带自由变量的广义几何规划(FGGP)问题广泛出现在证券投资和工程设计等实际问题中.利用等价转换及对目标函数和约束函数的凸下界估计,提出一种求(FGGP)问题全局解的凸松弛方法.与已有方法相比,方法可处理符号项中含有更多变量的(FGGP)问题,且在最后形成的凸松弛问题中含有更少的变量和约束,从而在计算上更容易实现.最后数值实验表明文中方法是可行和有效的.
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| 关 键 词： | 广义几何规划 自由变量 全局解 凸松弛 |
A New Approach for Solving Global Solution of Generalized Geometric Programming with Free Variables |
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| JIN Li
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LIU Hui-fang
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PEI Yong-gang.A New Approach for Solving Global Solution of Generalized Geometric Programming with Free Variables[J].Mathematics in Practice and Theory,2012,42(12):100-106. |
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| Authors: | JIN Li LIU Hui-fang PEI Yong-gang |
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| Institution: | 1.Deparment of Basic Science,Henan Mechanical and Electrical Engineering College,Xinxiang 453003,China) (2.College of Mahthematics and Information Science,Henan Normal University,Xinxiang 450001,China) |
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| Abstract: | Generalized geometric programming(FGGP)problems with free variables occur frequently in portfolio investment and engineering design.By utilizing equivalent transformation and the convex underestimate of the objective and constraint functions,a convex relaxation method is proposed for finding global solution of(FGGP).In comparison with the method presented,this approach can solve signomial terms with more variables of(FGGP), and the convex relaxed problem produced involves less variables and constraints,so it can be realized more easy in computation.The numerical experiments show the feasibility and efficiency of the proposed method. |
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| Keywords: | generalized geometric programming free variables global solution convex relaxation |
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