English

运筹学学报 ›› 2015, Vol. 19 ›› Issue (3): 48-56.doi: 10.15960/j.cnki.issn.1007-6093.2015.03.007

• 运筹学 • 上一篇    下一篇

无罚函数和滤子的一个新的QP-free方法

濮定国1,2, 尚有林1,*, 王关琳1   

  1. 1. 河南科技大学数学系，河南洛阳 , 471023; 2. 同济大学数学系， 上海,  200092
  • 收稿日期:2015-04-30 出版日期:2015-09-15 发布日期:2015-09-15
  • 通讯作者: 尚有林 mathshang@sina.com

A new QP-free method without a penalty function and a filter

PU Dingguo1,2, SHANG Youlin1,*, WANG Guanlin1   

  1. 1. Department of Mathematics, Henan University of Science and Technology, Henan Luoyang 471023, China; 2. Department of Mathematics, Tongji University, Shanghai 200092, China
  • Received:2015-04-30 Online:2015-09-15 Published:2015-09-15

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437

被引次数

1

摘要：

通过构造一个等价于原约束问题一阶KKT条件的非光滑方程组, 提出一类新的QP-free方法. 在迭代中采用了无罚函数和无滤子线搜索方法, 在此基础上, 通过牛顿-拟牛顿迭代得到满足KKT最优条件的解, 并证明该算法是可实现、具有全局收敛性. 另外, 在较弱条件下可以证明该方法具有超线性收敛性.

关键词: 滤子, QP-free方法, 约束, 收敛性, 非线性互补函数

Abstract:

 In this paper, we propose a new QP-free infeasible method based on the solution of nonsmooth equations which  are obtained by the multipliers and the piecewise linear relationship NCP function for the KKT first-order optimality conditions. We do not use  a penalty function and a filter on line search. Locally, each iteration of this method can be viewed as a perturbation of the mixed Newton-quasi Newton iteration on both  primal and dual variables for the solution of  KKT optimality conditions. This method is  implementable and globally convergent. Without the second  order correction we  prove that the  method has superlinear convergence rate under some mild conditions.

Key words: filter, QP-free , method, constraint, convergence, NCP function