| 半定规划与线性规划之异同 |
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| 引用本文： | 王建宏,孙建平,刘萌.半定规划与线性规划之异同[J].南通大学学报(自然科学版),2007,6(3):19-22. |
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| 作者姓名： | 王建宏 孙建平 刘萌 |
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| 作者单位： | 1. 南通大学,理学院,江苏,南通,226007
2. 上海交通大学,数学系,上海,200030 |
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| 基金项目： | 南通大学校科研和教改项目 |
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| 摘 要： | 文章对半定规划和线性规划问题进行比较研究,概括介绍了两者的异同点.半定规划是将线性规划中的向量变量用对称矩阵变量代替,非负约束用半正定约束代替而得到,因此半定规划与线性规划有很多相似之处,而半定规划比线性规划更一般.
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| 关 键 词： | 半定规划 线性规划 对偶 最优性条件 内点算法 |
| 文章编号： | 1673-2340（2007）03-0019-04 |
| 修稿时间： | 2006-07-07 |
The Similarities and Differences between Semidefinite Programming and Linear Programming |
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| Authors: | WANG Jian-hong SUN Jian-ping LIU Meng |
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| Institution: | 1.School of Sciences, Nantong University, Nantong 226007, China; 2. Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, China |
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| Abstract: | Semidefinite programming(SDP) arises from the well-known linear programming(LP) by replacing the vector of variables with a symmetric matrix and replacing the nonnegativity constraints with a positive semidefinite constraint.It is therefore not surprising to find many parallels between semidefinite and linear programming.Semidefinite programming,however,is much more general than linear programming.Here we will investigate these two classes of optimization problems and survey the similarities and differences between semidefinite programming and linear programming. |
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| Keywords: | semidefinite programming(SDP) linear programming(LP) duality optimality conditions interior-point algorithms |
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