具有带状系数矩阵的无限维线性规划的解法  

Method Of Solving Infinite Dimensional Linear Programming with Infinite Band Coefficient Matrix

作　　者：李大林[1] 黄雪燕[2] 赵展辉[3] 

机构地区：[1]柳州职业技术学院基础部,广西柳州545006 [2]钦州学院数学与计算机科学系,广西钦州535000 [3]广西工学院信息与计算科学系,广西柳州545006

出　　处：《大学数学》2011年第2期99-103,共5页College Mathematics

基　　金：广西教育厅科研项目(200707LZ259)

摘　　要：研究一类每个约束条件有两个变量且每个变量出现在两个约束条件中的无限维线性规划.引入松弛变量后,得到约束方程组的系数矩阵为无限阶带状矩阵,用它的左逆以及属于零的特征向量可以表示这类问题的最优解.获得目标函数值收敛的一个充分条件.We consider the class of infinite dimensional linear programs with constraints having the property that every constraint contains two variables while every variable appears in two constraints.With the introduction of slack variables,the constrained infinite linear equations has been obtained,whose coefficient matrix is an infinite order band matrix.Thus the optimal solution of such a problem is expressed by the left inverse and the eigenvectors corresponding to the zero eigenvalue of this matrix.A sufficient condition is got for the convergence of the objective function.

关 键 词：无限维线性规划 无限阶带状矩阵 最优解 

分 类 号：O232[理学—运筹学与控制论]