| 线性权互补问题的新全牛顿步可行内点算法 |
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| 引用本文： | 迟晓妮,张睿婕,刘三阳.线性权互补问题的新全牛顿步可行内点算法[J].应用数学,2021,34(2):304-311. |
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| 作者姓名： | 迟晓妮 张睿婕 刘三阳 |
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| 作者单位： | 1. 桂林电子科技大学数学与计算科学学院, 广西 桂林 541004; 2. 桂林电子科技大学广西密码学与信息安全重点实验室, 广西 桂林 541004; 3. 桂林电子科技大学广西自动检测技术与仪器重点实验室, 广西 桂林 541004; 4. 西安电子科技大学数学与统计学院, 陕西 西安 710071 |
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| 基金项目： | 国家自然科学基金(11861026,61877046);广西密码学与信息安全重点实验室研究课题(GCIS201819);广西自动检测技术与仪器重点实验室基金(YQ18112,YQ19111)。 |
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| 摘 要： | 基于一个连续可微函数,通过等价变换中心路径,给出求解线性权互补问题的一个新全牛顿步可行内点算法.该算法每步迭代只需求解一个线性方程组,且不需要进行线搜索.通过适当选取参数,分析了迭代点的严格可行性,并证明算法具有线性优化最好的多项式时间迭代复杂度.数值结果验证了算法的有效性.
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| 关 键 词： | 线性权互补问题 可行内点算法 新全牛顿步 迭代复杂度 |
| 收稿时间： | 2020/4/4 0:00:00 |
A New Full-Newton Step Feasible Interior-Point Algorithm for Linear Weighted Complementarity Problem |
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| CHI Xiaoni,ZHANG Ruijie,LIU Sanyang.A New Full-Newton Step Feasible Interior-Point Algorithm for Linear Weighted Complementarity Problem[J].Mathematica Applicata,2021,34(2):304-311. |
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| Authors: | CHI Xiaoni ZHANG Ruijie LIU Sanyang |
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| Institution: | (School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China;Guangxi Key Laboratory of Cryptography and Information Security,Guilin University of Electronic Technology,Guilin 541004,China;Guangxi Key Laboratory of Automatic Detecting Technology and Instruments,Guilin University of Electronic Technology,Guilin 541004,China;School of Mathematics and Statistics,Xidian University,Xi'an 710071,China) |
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| Abstract: | Based on a continuously differentiable function,a new full-Newton step feasible interiorpoint algorithm for the linear weighted complementarity problem is proposed by the equivalent transformation of central path.In each iteration,only one linear system of equations is required to be solved without any line search.By choosing appropriate parameters,we show that the iteration points are strictly feasible and the iteration complexity bound is a good as the best-known complexity for linear optimization.The numerical results illustrate that the algorithm is effective. |
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| Keywords: | Linear weighted complementarity problem Feasible interior-point algorithm New full-Newton step Iteration complexity |
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