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一种基于LVI求解二次规划问题的数值算法
  • ISSN号：1007-6093
  • 期刊名称：运筹学学报
  • 时间：2012
  • 页码：21-30
  • 分类：O221.2[理学—运筹学与控制论;理学—数学]
  • 作者机构：[1]中山大学信息科学与技术学院,广州510006, [2]中山大学深圳研究院,深圳518057, [3]中山大学软件学院,广州510006
  • 相关基金：supported by The National Natural Science Foundation of China(No61075121, 60935001);by the Fundamental Research Funds for the Central Universities of China(No3162460)
  • 相关项目：面向服务任务的快速机器视觉与智能伺服控制
作者： 张雨浓|李学忠|张智军|李钧|
关键词： 数值算法, 二次规划, 94LVI算法, 全局收敛性, numerical algorithm, quadratic programming, 94LVI algorithm, global convergence
中文摘要：

给出并研究了一种数值算法（简称94LVI算法）,用于求解带等式和双端约束的二次规划问题.这类带约束的二次规划问题首先被转换为线性变分不等式问题,该问题等价于分段线性投影等式.接着使用94LVI算法求解上述分段线性投影等式,从而得到QP问题的最优解.进一步给出了94LVI算法的全局收敛性证明.94LVI算法与经典有效集算法的对比实验结果证实了给出的94LVI算法在求解二次规划问题上的高效性与优越性.

英文摘要：

This paper presents and investigates a numerical algorithm （termed as 94LVI algorithm） for solving quadratic programming （QP） problems with linear equality and bound constraints. To do this, the constrained QP problems are firstly converted into linear variational inequalities （LVI）, which are then converted into equivalent piecewise- linear projection equations （PLPE）. After that, the resultant PLPE is solved by the presented 94LVI algorithm. The optimal numerical solutions to the QP problems are thus obtained. Furthermore, the theoretical proof of the global convergence of the 94LVI algorithm is presented. The numerical comparison results between the 94LVI algorithm and the active set algorithm are provided as well, which further demonstrates the efficacy and superiority of the presented algorithm for solving such QP problems.

同期刊论文项目
面向服务任务的快速机器视觉与智能伺服控制
期刊论文 152 会议论文 19
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期刊信息
  • 《运筹学学报》
  • 中国科技核心期刊
  • 主管单位:中国科学技术协会
  • 主办单位:中国运筹学会
  • 主编：胡旭东
  • 地址：上海市上大路99号上海大学期刊社
  • 邮编：200444
  • 邮箱：ort@mail.shu.edu.cn
  • 电话：021-66137605
  • 国际标准刊号：ISSN：1007-6093
  • 国内统一刊号：ISSN：31-1732/O1
  • 邮发代号:4-777
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）
  • 被引量:1362