| 一个解半正定规划问题的基于广义对数障碍函数的原始对偶内点算法 |
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| 引用本文： | 滕开选,白延琴,王国强. 一个解半正定规划问题的基于广义对数障碍函数的原始对偶内点算法[J]. 应用数学与计算数学学报, 2007, 21(2): 62-72 |
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| 作者姓名： | 滕开选 白延琴 王国强 |
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| 作者单位： | 1. 上海大学理学院数学系,上海,200444
2. 上海工程技术大学高职学院,上海,200437 |
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| 摘 要： | 本文对经典对数障碍函数推广,给出了一个广义对数障碍函数.基于这个广义对数障碍函数设计了解半正定规划问题的原始-对偶内点算法.分析了该算法的复杂性,得到了一个理论迭代界,它与已有的基于经典对数障碍函数的算法的理论迭代界一致.同时,并给出了一个数值算例,阐明了函数的参数对算法运行时间的影响.
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| 关 键 词： | 半正定规划 原始-对偶内点算法 大步校正方法和小步校正方法 |
| 修稿时间： | 2006-04-04 |
A Primal-Dual Interior-Point Algorithm for Semidefinite Optimization Based on a Generalized Logarithmic Barrier Function |
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| Teng Kaixuan,Bai Yanqin,Wang Guoqiang. A Primal-Dual Interior-Point Algorithm for Semidefinite Optimization Based on a Generalized Logarithmic Barrier Function[J]. Communication on Applied Mathematics and Computation, 2007, 21(2): 62-72 |
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| Authors: | Teng Kaixuan Bai Yanqin Wang Guoqiang |
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| Abstract: | In this article,we extend the classic logarithmic barrier function to a generalized one and present a primal-dual interior algorithm based on this function.We derive the iteration bound of algorithm for both large-update and small-update methods. They are the same as those based on the classical logarithmic barrier function.We provide a numerical example which illustrates how the parameter impacts the iteration bound of the algorithm. |
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| Keywords: | semidefinite optimization primal-dual interior-point methods large-and small-update methods |
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