带自由变量的广义几何规划全局求解的新算法  

A New Approach for Solving Global Solution of Generalized Geometric Programming with Free Variables

作　　者：靳利[1] 刘慧芳[1] 裴永刚[2] 

机构地区：[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

出　　处：《数学的实践与认识》2012年第12期100-106,共7页Mathematics in Practice and Theory

基　　金：河南省教育厅自然科学研究计划项目(2011B110012;12B110004)

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.Generalized geometric programming （FGGP） frequently in portfolio investment and engineering design problems with free variables occur By utilizing equivalent transfor marion and the convex underestilnate 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.

关 键 词：广义几何规划 自由变量 全局解 凸松弛 

分 类 号：O221.2[理学—运筹学与控制论]