带有新的迭代格式的内点算法

杨喜美; 刘红卫; 张因奎

doi:10.3879/j.issn.1000-0887.2014.09.012

带有新的迭代格式的内点算法

doi: 10.3879/j.issn.1000-0887.2014.09.012

¹河南师范大学数学与信息科学学院, 河南新乡 453007;²西安电子科技大学数学与统计学院, 西安 710071

基金项目: 国家自然科学基金(61179040; 61303030); 广西高校科研重点项目资助(ZD2014050)

详细信息

作者简介:
杨喜美(1982—)，女，河南周口人，博士(通讯作者. E-mail: yangximeiluoyang@126.com);刘红卫(1967—)，男，陕西渭南人，教授(E-mail: liuhongweixidian@126.com);张因奎(1983—)，男，河南信阳人，硕士(E-mail: yangximeixidian@126.com).

中图分类号: O221.1
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出版历程
- 收稿日期: 2013-12-24
- 刊出日期: 2014-09-15

An Interior-Point Method With a New Iterative Scheme

¹College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, P.R.China;²School of Mathematics and Statistics, Xidian University, Xi’an 710071, P.R.China

Funds: The National Natural Science Foundation of China(61179040； 61303030)

摘要

摘要: 研究了求解线性规划问题的二阶Mehrotra型预估矫正内点算法,使用Newton方法求解预估方向和矫正方向,并利用两个方向的一种新的组合方式得到搜索方向.在每次迭代中，要求新的迭代点在中心路径的一个宽邻域内,从而计算出步长参数.通过分析,证明了该算法经过有限次迭代后收敛到问题的一个最优解,并具目前内点算法最好的多项式复杂度O(√nL).数值实验表明该算法在实践中是有效的.
- 线性规划 /
- 内点算法 /
- 迭代格式 /
- 宽邻域 /
- 多项式复杂度
Abstract: A 2nd-order Mehrotra-type predictor-corrector interior-point method was proposed for linear programming, in which the predictor direction and corrector direction were computed with the Newton method and the search direction was obtained through a new form of combination of the predictor direction and corrector direction. At each step of the iteration, the step size parameter was calculated with the iteration restricted to a wide neighborhood of the central path. Analysis indicates the proposed algorithm converges to the optimal solution after finite times of iteration and has the polynomial iteration complexity O(√nL), which is the best complexity result for the current interior-point methods. Numerical experiment proves the high efficiency of the proposed algorithm.
- linear programming /
- interior-point method /
- iterative scheme /
- wide neighborhood /
- polynomial complexity

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参考文献(17)

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