Linear programming with positive semi definite matrices
Linear programming with positive semi definite matrices
复制标题
正半定矩阵的线性规划
DOI：
10.1109/cdc.1995.480242
复制
发表时间：
1995
期刊：
影响因子：
--
通讯作者：
Jean B. Lasserre
中科院分区：
文献类型：
--
作者：
Jean B. Lasserre
我们考虑正半定矩阵圆锥上的一般线性规划问题。我们首先提供存在最优解且不存在对偶间隙的简单充分条件，而不需要存在严格可行的解。然后，我们简单地描述线性规划标准概念的类似物，即极值点、基、降低成本、简并性、旋转步骤以及类似单纯形的算法。
We consider the general linear programming problem over the cone of positive semi-definite matrices. We first provide a simple sufficient condition for existence of optimal solutions and absence of a duality gap without requiring existence of a strictly feasible solution. We then simply characterize the analogues of the standard concepts of linear programming, i.e., extreme points, basis, reduced cost, degeneracy, pivoting step as well as a simplex-like algorithm.