摘要
其中,A是秩为m的m×n矩阵,m<n;b=(b_1,…,b_m)~T;C=(c_1,…,c_n);X=(x_1,…,x_n)~T。管梅谷、郑汉鼎在[1]中指出:非退化的基可行解X^0是(L)唯一最优解的充分必要条件是X^0的所有非基变量的检验数小于零,陶惠民在[2]中指出:退化的基可行解X^0是(L)的唯一最优解的充分必要条件是X^0的所有非基变量的检验数小于零。本文讨论在非基变量有零检验数时基最优解X^0是(L)的唯一基最优解的条件,其次证明了(L)的最优解集是一个凸多面体,最后指出基最优解的最少个数。设基最优解X^0对应的单纯形表为:
Guam Meigu, Zheng Handing and Tao Huimin pointed out that the sufficient and necessary condition of which a basic feasible solution is the unique optimal solution for linear programming (L).
In this paper we have proved sufficient condition of which a basic optimal solution is the unique basic optimal solution of (L). Then we have proved the optimal solution set of (L) is a convex polyhedron, a optimal solution of (L) can be is represeted as the sum of convex combination of optimal extreme points and nonnegative linear combination of optimal extreme direction of feasible solution set of (L). Finally we pointed out the fewest numbers of basic optimal solution of (L).
出处
《应用数学与计算数学学报》
1992年第1期86-91,共6页
Communication on Applied Mathematics and Computation
