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张立卫 教授

张立卫,分别于1989年7月,1992年7月,1998年7月在大连理工大学应用数学系获得理学学士学位,运筹学与控制论专业硕士学位,计算数学博士学位,研究生导师是夏尊铨教授。1992年硕士毕业后在大连理工大学应用数学系工作至今,他1995年被评为副教授,1999年被评为教授,2002年被评为运筹学与控制论专业博士生导师,2005年被评为金融数学与保险精算专业博士生导师。他现在是大连理工大学数学科学学院的教授,博士生导师。 张立卫目前的研究兴趣是“随机优化”,“矩阵优化”,“变分分析”和“均衡优化”,在这些方向上发表SCI检索论文100余篇,其中有论文发表在运筹学与计算数学的顶级期刊上,这些期刊包括Operations Research, Mathematical Pr...

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A Regularized Semi-Smooth Newton Method with Projection Steps for Composite Convex Programs

发布时间: 2019-03-12 点击量:

  • 论文类型:期刊论文
  • 第一作者:Xiao, Xiantao
  • 通讯作者:Wen, ZW (reprint author), Peking Univ, Beijing Int Ctr Math Res, Beijing, Peoples R China.
  • 合写作者:Li, Yongfeng,Wen, Zaiwen,Zhang, Liwei
  • 发表刊物:JOURNAL OF SCIENTIFIC COMPUTING
  • 收录刊物:SCIE
  • 卷号:76
  • 期号:1
  • 页面范围:364-389
  • ISSN号:0885-7474
  • 关键字:Composite convex programs; Operator splitting methods; Proximal mapping; Semi-smoothness; Newton method
  • 摘要:The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: (1) Many well-known operator splitting methods, such as forward-backward splitting and Douglas-Rachford splitting, actually define a fixed-point mapping; (2) The optimal solutions of the composite convex program and the solutions of a system of nonlinear equations derived from the fixed-point mapping are equivalent. Solving this kind of system of nonlinear equations enables us to develop second-order type methods. These nonlinear equations may be non-differentiable, but they are often semi-smooth and their generalized Jacobian matrix is positive semidefinite due to monotonicity. By combining with a regularization approach and a known hyperplane projection technique, we propose an adaptive semi-smooth Newton method and establish its convergence to global optimality. Preliminary numerical results on -minimization problems demonstrate that our second-order type algorithms are able to achieve superlinear or quadratic convergence.
  • 发表时间:2018-07-01