| LMI优化问题的择一性定理与对偶 |
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| 引用本文： | 王建宏. LMI优化问题的择一性定理与对偶[J]. 大学数学, 2011, 27(1): 29-34 |
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| 作者姓名： | 王建宏 |
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| 作者单位： | 南通大学,理学院,江苏,南通,226007 |
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| 基金项目： | The Nature Science Foundation of China，The Nature Science Foundation of Universities，Jiangsu Province Educational Science Eleventh Five-Year Plan Foundation，Jiangsu Modern Educational Technology Research Foundation，the Nature Science Foundation，Nantong University and the Humanities and Social Sciences Youth Fund of Education Ministry |
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| 摘 要： | 考虑目标函数是线性函数约束条件为线性矩阵不等式的LMI优化问题,讨论了LMI优化问题中的四个择一性定理.每种类型的择一性定理包含两个线性不等式和(或)等式系统,一个原始系统和一个对偶系统.弱择一性定理说明两系统中至多只有其一有解;基于凸集分离理论得到的强择一性定理说明两系统有且仅有其一有解.并在此基础上推导了LMI优化...
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| 关 键 词： | 弱择一性 强择一性 弱对偶 强对偶 线性矩阵不等式 LMI优化问题 |
Theorems of the Alternative and Duality for LMI Optimization |
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| WANG Jian-hong. Theorems of the Alternative and Duality for LMI Optimization[J]. College Mathematics, 2011, 27(1): 29-34 |
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| Authors: | WANG Jian-hong |
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| Affiliation: | WANG Jian-hong(School of Science,Nantong University,Nantong,Jiangsu 226007,China) |
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| Abstract: | We consider the minimization of a linear objective subject to linear matrix inequality constraints(LMI optimization).Four alternative theorems for LMI optimization are discussed,which are very important for the analysis of the duality theory of LMI optimization.Every typical alternative theorem is associated with two systems of linear inequalities and(or) equalities,a primal system and a dual one.The weak alternative theorems assert that two systems at most one of which has a solution.The strong alternative... |
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| Keywords: | weak alternative strong alternative weak duality strong duality linear matrix inequality LMI optimization |
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