| 基于一个有限罚函数的二阶锥优化的原始-对偶内点算法 |
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| 引用本文： | 王国强. 基于一个有限罚函数的二阶锥优化的原始-对偶内点算法[J]. 运筹学学报, 2007, 11(2): 31-42 |
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| 作者姓名： | 王国强 |
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| 作者单位： | 上海工程技术大学高职学院,上海,200437;上海大学数学系,上海,200444 |
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| 摘 要： | 本文基于一个有限罚函数,设计了关于二阶锥优化问题的原始-对偶路径跟踪内点算法,由于该罚函数在可行域的边界取有限值,因而它不是常规的罚函数,尽管如此,它良好的解析性质使得我们能分析算法并得到基于大步校正和小步校正方法目前较好的多项式时间复杂性分别为O(N~(1/2)log N log N/ε)和O(N~(1/2)log N/ε),其中N为二阶锥的个数．
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| 关 键 词： | 运筹学 二阶锥优化 原始-对偶内点算法 大步和小步校正方法 |
| 修稿时间： | 2006-03-05 |
Primal-Dual Interior-Point Algorithm for Second-Order Cone Optimization Based on a Finite Barrier |
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| Wang Guoqiang. Primal-Dual Interior-Point Algorithm for Second-Order Cone Optimization Based on a Finite Barrier[J]. OR Transactions, 2007, 11(2): 31-42 |
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| Authors: | Wang Guoqiang |
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| Affiliation: | 1. College of Vocational Technology, Shanghai University of Engineering Science, Shanghai 200437;2. Department of Mathematics, Shanghai University, Shanghai 200444, China |
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| Abstract: | In this paper we present a primal-dual path-following interior-point algorithm for second-order cone optimization based on a finite barrier function which was first introduced in [2]. The barrier function is not a conventional one because it takes the finite value at the boundary of the feasible region. We analyze the algorithm and obtain the favorable complexity bounds of the algorithm in terms of the elegant analytic properties of the finite barrier function. The complexity bounds for large- and small-update methods are O(√N log N logN/ε) and O(√N log N/ε), respectively, where N denotes the number of second-order cones. |
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| Keywords: | Operations research second-order cone optimization interior-point algorithm large-and small-update methods |
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