| 摘要: |
| 本文提出求解二次半定规划的一个基于H..K..M方向的原始对偶路径跟踪算法.文中首先导出确定H..K..M方向的线性方程组,并证明该搜索方向的存在唯一性;然后给出算法的具体步骤,并证明算法产生的迭代点列落在中心路径的某个邻域内.最后采用Matlab (R2011b)数学软件编程对算法进行数值试验.数值结果表明算法是有效的. |
| 关键词: 二次半定规划 原始对偶 算法 路径跟踪 中心路径 |
| DOI：10.13656/j.cnki.gxkx.20161121.007 |
| 投稿时间：2016-08-05修订日期：2016-09-25 |
| 基金项目:国家自然科学基金项目(No.11561005)和广西自然科学基金项目(2016GXNSFAA380248,2014GXSFFA118001)资助。 |
|
| A Primal-dual Path-following Algorithm for Quadratic Semi-definite Programming |
|
LI Jianling, WANG Peipei
|
| (College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, China) |
| Abstract: |
| A primal-dual path-following algorithm based on H..K..M direction for quadratic semi-definite programming problems(QSDP) is proposed.Firstly,the system of linear equations yielding the H..K..M direction are derived,and the existence and uniqueness of the search direction are shown;Secondly,the algorithm is described in detail.We show that the iterates generated by the algorithm can fall into some neighborhood of the central path under some mild conditions.Finally,a preliminary numerical experiment is performed for the algorithm by using Matlab (R2011b) mathematical software,and the numerical results show that the proposed algorithm is effective. |
| Key words: quadratic semi-definite programming primal-dual algorithm path-following central path |
