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运筹学学报 ›› 2013, Vol. 17 ›› Issue (1): 106-116.

• 运筹学 • 上一篇    下一篇

无罚函数和滤子的QP-free非可行域方法

濮定国1,2，刘爱兰2,3，尚有林1，冯爱芬1，孙振洋1   

  1. 1. 河南科技大学数学系 2. 同济大学数学系 3. 上海电力学院数理学院
  • 出版日期:2013-03-15 发布日期:2013-03-15
  • 通讯作者: 濮定国 E-mail:madpu@tongji.edu.cn

QP-free  infeasible method without a penalty function and a filter

PU Dingguo1,2, LIU Ailan2,3, SHANG Youlin1, FENG Aifen1, SUN Zhenyang1   

  1. 1.  Department of Mathematics, Henan University of Science and Technology 2. Department of Mathematics, Tongji University 3. School of Mathematics and Physics, Shanghai University of Electric Power
  • Online:2013-03-15 Published:2013-03-15

PDF

956

被引次数

23

摘要： 提出了求解光滑不等式约束最优化问题的无罚函数和无滤子QP-free非可行域方法. 通过乘子和非线性互补函数, 构造一个等价于原约束问题一阶KKT条件的非光滑方程组. 在此基础上, 通过牛顿-拟牛顿迭代得到满足KKT最优性条件的解, 在迭代中采用了无罚函数和无滤子线搜索方法, 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非可行域方法, 收敛性, 约束, 非线性互补函数

Abstract: In this paper, we propose a  QP-free infeasible method without a penalty function and a filter  for constrained nonlinear optimization  problems. This iterative method is  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.  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. We do not  use  a penalty function and a filter on line searches. 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