数学物理学报 ›› 2012, Vol. 32 ›› Issue (2): 336-343.

• 论文 • 上一篇    下一篇

修正的SQP型并行变量分配算法

冯婷婷1, 韩丛英1, 2**, 贺国平1   

  1. 1.山东科技大学信息科学与工程学院 山东青岛 266510|
    2.中国科学院研究生院数学科学学院 北京 100049
  • 收稿日期:2010-11-21 修回日期:2011-12-30 出版日期:2012-04-25 发布日期:2012-04-25
  • 通讯作者: 韩丛英,congyh@sdust.edu.cn E-mail:fuchen_ftt@163.com; congyh@sdust.edu.cn; hegp@263.net
  • 基金资助:

    国家自然科学基金(11101420, 10971122)、高等学校博士点基金(20093718110005)、山东省科技攻关(2009GG10001012)和山东省自然科学基金(Y2008A01)资助

A Modified SQP Parallel Variable Distribution Algorithm

 FENG Ting-Ting1, HAN Cong-Ying1, 2**, HE Guo-Ping1   

  1. 1.College of Information Science and Technology, Shandong University of Science and Technology, Shandong |Qingdao 266510;
    2.School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049
  • Received:2010-11-21 Revised:2011-12-30 Online:2012-04-25 Published:2012-04-25
  • Contact: HAN Cong-Ying,congyh@sdust.edu.cn E-mail:fuchen_ftt@163.com; congyh@sdust.edu.cn; hegp@263.net
  • Supported by:

    国家自然科学基金(11101420, 10971122)、高等学校博士点基金(20093718110005)、山东省科技攻关(2009GG10001012)和山东省自然科学基金(Y2008A01)资助

摘要:

Ferris 和Mangasarian 提出求解最优化问题的PVD(并行变量分配)算法, 此算法是把变量分为主要变量和辅助变量, 分配到p个处理机上, 每个处理机除了负责更新本处理机的主要变量外, 同时还沿着给定的方向更新辅助变量, 使算法的鲁棒性和灵活性得到了很大的提高. 该文基于文献[6]提出一种修正的SQP型PVD算法, 构造其搜索方向是下降方向和可行方向的组合, 并对此方向给予一个高阶修正, 使此算法很好地防止 Maratos 效应发生, 而且能够克服在求解子问题时出现约束不相容的情况. 在合适的条件下, 推导出此算法具有全局收敛性.

关键词: 非线性规划, 序列二次规划, PVD算法

Abstract:

Ferris and Mangasarian proposed a PVD(parallel variable distribution) algorithm for solving optimization problems, which divides variables into primary and secondary variables groups. According to the algorithm, the variables are distributed among p parallel processors with each processor having the responsibility for updating its primary variables while allowing the remaining "secondary" variables to change in a restricted fashion along some easily computable directions, which enhances robustness and flexibility of the algorithm. In this paper, we present a modified SQP type PVD algorithm based on [6], whose search direction is a suitable combination of a descent direction and a feasible direction, and give a second-order revised for such a  direction. This new algorithm is very effective in preventing Maratos effect from happening, and avoid constraints in subproblem are inconsistent. We show the global convergence under some suitable conditions.

Key words: Nonlinear programming, Sequential quadratic programming, PVD algorithm

中图分类号: 

  • 46N10