EXPLICIT SOLUTIONS FOR INTERVAL SEMIDEFINITE LINEAR PROGRAMS
EXPLICIT SOLUTIONS FOR INTERVAL SEMIDEFINITE LINEAR PROGRAMS
复制标题
区间半定线性规划的显式解
DOI：
10.1016/0024-3795(94)00130-8
复制
发表时间：
1996
影响因子：
1.1
通讯作者：
Henry Wolkowicz
中科院分区：
文献类型：
--
作者：
Henry Wolkowicz
我们考虑一类特殊的半定线性规划[公式：见文本]，其中C， X， L， U是对称矩阵，A是一个（映上）线性算子，⪯表示Löwner（正半定）偏序。给出了一般最优解和对偶最优解的显式表示。这扩展了Ben-Israel和Charnes[3]中出现的标准线性规划的结果。这项工作受到Yang和Vanderbei b[15]最近提出的另一类半确定问题的显式解的进一步激励。
We consider the special class of semidefinite linear programs [Formula: see text] , where C, X, L, U are symmetric matrices, A is an (onto) linear operator, and ⪯ denotes the Löwner (positive semidefinite) partial order. We present explicit representations for the general primal and dual optimal solutions. This extends the results for standard linear programming that appeared in Ben-Israel and Charnes [3]. This work is further motivated by the explicit solutions for a different class of semidefinite problems presented recently in Yang and Vanderbei [15].