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线性约束两分块非凸优化的ADMM-SQP算法

简金宝1,2,* 劳译娴1  晁绵涛1 马国栋3   

  1. 1. 广西大学数学与信息科学学院, 南宁  530004; 2. 广西民族大学理学院, 南宁  530007; 3. 玉林师范学院数学与统计学院, 广西高校复杂系统优化与大数据重点实验室, 广西 玉林 537000
  • 收稿日期:2017-11-08 出版日期:2018-06-15 发布日期:2018-06-15
  • 通讯作者: 简金宝 E-mail: jianjb@gxu.edu.cn
  • 基金资助:

    国家自然科学基金 (Nos. 11771383, 11601095), 广西自然科学基金 (Nos. 2016GXNSFDA380019, 2016GXNSFBA380185)

ADMM-SQP algorithm for two blocks linear constrained nonconvex optimization

JIAN Jinbao1,2,*  LAO Yixian1 CHAO Miantao1 MA Guodong3   

  1. 1. College of Mathematics and Information Science, Guangxi University, Nanning 530004, China; 2. College of Science, Guangxi University of Nationalities, Nanning 530007, China; 3. School of Mathematics and Statistics, Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, Guangxi,  China
  • Received:2017-11-08 Online:2018-06-15 Published:2018-06-15

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摘要：

基于乘子交替方向法(ADMM)和序列二次规划(SQP)方法思想, 致力于研究线 性约束两分块非凸优化的新型高效算法. 首先, 以SQP思想为主线, 在其二次规划(QP)子问题的求解中引入ADMM思想, 将QP分解为两个相互独立的小规模QP求解. 其次, 借助增广拉格朗日函数和Armijo线搜索产生原始变量新迭代点. 最后, 以显式解析式更新对偶变量. 因此, 构建了一个新型ADMM-SQP算法. 在较弱条件下, 分析了算法通常意义下的全局收敛性, 并对算法进行了初步的数值试验.

关键词: 线性约束, 两分块非凸优化, 乘子交替方向法, 序列二次规划, 算法

Abstract:

Based on the alternating direction method of multipliers (ADMM) and the sequential quadratic programming (SQP) method, this paper proposes a new efficient algorithm for two blocks nonconvex optimization with linear constrained. Firstly, taking SQP thought as the main line, the quadratic programming (QP)  is decomposed into two independent small scale QP according to ADMM idea. Secondly, the new iteration point of the prime variable is generated by Armijo line search  for the augmented Lagrange function. Finally, the dual variables are updated by an explicit expression. Thus, a new ADMM-SQP algorithm is constructed. Under the weaker conditions, the global convergence of the  algorithm is analyzed. Some preliminary numerical results  are reported to support the efficiency of the new algorithm.

Key words: linear constrained, two blocks nonconvex optimization, alternating direction method of multipliers, sequential quadratic programming method, algorithm