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(槡nL).数值实验表明该算法在实践中是有效的.
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 combina- tion 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.
出处
《应用数学和力学》
CSCD
北大核心
2014年第9期1063-1070,共8页
Applied Mathematics and Mechanics
基金
国家自然科学基金(61179040
61303030)
广西高校科研重点项目资助(ZD2014050)~~
关键词
线性规划
内点算法
迭代格式
宽邻域
多项式复杂度
linear programming
interior-point method
iterative scheme
wide neighborhood
polynomial complexity