基于核函数求解 LCPs的全-Newton步不可行内点算法

陈月姣, 张明望

数学学报 ›› 2014, Vol. 57 ›› Issue (6) : 1047-1060.

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PDF(624 KB)
数学学报 ›› 2014, Vol. 57 ›› Issue (6) : 1047-1060. DOI: 10.12386/A2014sxxb0097
论文

基于核函数求解 LCPs的全-Newton步不可行内点算法

    陈月姣, 张明望
作者信息 +

A Full-Newton Step Infeasible Interior-Point Algorithm for LCPs Based on a Kernel Function

    Yue Jiao CHEN, Ming Wang ZHANG
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文章历史 +

摘要

本文对P*(k)线性互补问题设计了一种基于核函数的全-Newton步不可行内点算法,是对Mansouri等人提出的单调线性互补问题全-Newton步不可行内点算法的改进与推广.算法的主迭代由一个可行步和几个中心步构成且可行步采用小步校正.通过建立和应用一些新的技术性结果, 证明了算法的多项式复杂性为O((1+2k)3/2 (log2 log2 64(1+2k))n log max{(x0)T s0, ‖r0‖}/ε),当k=0时,与当前单调线性互补问题的不可行内点算法最好的迭代复杂性界一致.最后, 用 Matlab 数值实验验证了算法的可行性.

Abstract

In this paper a full-Newton step infeasible interior-point algorithm for P*k linear complementarity problems based on a kernel function is presented, the proposed algorithm is an extension of the infeasible interior-point method for monotone linear complementarity introduced by Mansouri.The main iteration of the algorithm consists of a feasibility step with small-update and several centrality steps.By establishing and using some new technical results, the polynomial complexity bound for the algorithm is obtained, namely, O((1+2k)3/2 (log2 log2 64(1+2k))n log max{(x0)T s0, ‖r0‖}/ε), which coincides with the currently best iteration bound for infeasible interior-point methods of monotone linear complementarity problems when k = 0.Finally, some preliminarily numerical results are presented to verify the feasibility of the proposed algorithm.

关键词

线性互补问题 / 不可行内点算法 / 全-Newton步 / 多项式复杂性 / 核函数

Key words

linear complementarity problem / infeasible interior-point algorithms / full- Newton step / polynomial complexity / kernel function

引用本文

导出引用
陈月姣, 张明望. 基于核函数求解 LCPs的全-Newton步不可行内点算法. 数学学报, 2014, 57(6): 1047-1060 https://doi.org/10.12386/A2014sxxb0097
Yue Jiao CHEN, Ming Wang ZHANG. A Full-Newton Step Infeasible Interior-Point Algorithm for LCPs Based on a Kernel Function. Acta Mathematica Sinica, Chinese Series, 2014, 57(6): 1047-1060 https://doi.org/10.12386/A2014sxxb0097

参考文献

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基金

湖北省自然科学基金资助项目(2008CDZ047)

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