| 自反Banach空间中锥线性优化问题初始——对偶目标函数水平集的几何性质 |
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| 引用本文： | 王焱,宋文.自反Banach空间中锥线性优化问题初始——对偶目标函数水平集的几何性质[J].应用泛函分析学报,2009,11(1):33-38. |
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| 作者姓名： | 王焱 宋文 |
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| 作者单位： | 1. 齐齐哈尔大学数学系,齐齐哈尔,161006
2. 哈尔滨师范大学数学科学学院,哈尔滨,150080 |
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| 基金项目： | 国家自然科学基金，黑龙江省杰出青年基金 |
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| 摘 要： | 讨论自反Banach空间中的原——对偶锥线性优化问题的目标函数水平集的几何性质．在自反Banach空间中，证明了原目标函数水平集的最大模与对偶目标函数水平集的最大内切球半径几乎是成反比例的．
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| 关 键 词： | 自反Banach空间 锥线性优化 对偶 水平集 |
The Geometry Property of the Primal-Dual Objective Function Level Sets on Conic Optimization in Reflexive Banach Spaces |
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| WANG Yan,SONG Wen.The Geometry Property of the Primal-Dual Objective Function Level Sets on Conic Optimization in Reflexive Banach Spaces[J].Acta Analysis Functionalis Applicata,2009,11(1):33-38. |
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| Authors: | WANG Yan SONG Wen |
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| Institution: | 1.Department of Mathematics, Qiqihar University, Qiqihar 161006, China;2.School of Mathematical Sciences, Harbin Normal University, Harbin 150080,China) |
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| Abstract: | We present a geometric relationship between the primal objective function level sets and the dual objective function level sets, for conic linear optimization. In reflexive Banach spaces, we prove that the maximum norms of the primal objective function level sets are nearly inversely proportional to the maximum inscribed radii of the dual objective function level sets. |
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| Keywords: | reflexive Banach spaces conic linear optimization duality level sets |
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