【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.更多还原

【Abstract】 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.更多还原