中文

Operations Research Transactions >

2015 , Vol. 19 >Issue 3: 48 - 56

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2015.03.007

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

Expand
  • 1. Department of Mathematics, Henan University of Science and Technology, Henan Luoyang 471023, China; 2. Department of Mathematics, Tongji University, Shanghai 200092, China

Received date: 2015-04-30

  Online published: 2015-09-15

Fold

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

Cite this article

PU Dingguo, SHANG Youlin, WANG Guanlin . A new QP-free method without a penalty function and a filter[J]. Operations Research Transactions, 2015 , 19(3) : 48 -56 . DOI: 10.15960/j.cnki.issn.1007-6093.2015.03.007

References

Pu D,  Li K,  Xue W. Convergence of QP-free infeasible methods for r inequality optimization problems [J]. J.of Tongji University, 2005, 33: 525-529.
Pu D,  Zhou Y, Zhang  Z. A QP free feasible method [J]. J. Comput. Math., 2004, {\bf 22}: 651-660.
Qi  H,  Qi L. A new QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization [J]. SIAM J.Optim., 2000,  11: 113-132.
Fletcher R,  Leyffer S, Toint P. On the global convergence of a filter-SQP algorithm [J].  SIAM J. Optim.,  2002, 12:  44-59.
Pu D,  Jin Z. Nonmonotone line search technique for QP-free infeasible method [J].  J. of Tongji University, 2010,  38: 311-316.
Ribeiro A,  Karas E W,  Gonzaga C C.  Global convergence of filter methods for nonlinear programming [J].  SIAM J. on Optimization, 2008, 19: 1231-1249.
Liu X,  Yuan Y.  A sequential quqdratic programming method  a penalty function and a filter for equality constrained nonlinear programming [J].  SIAM J. on Optimization,2011,  91: 545-571.
Ulbrich M, Ulbrich S. Non-monotone trust region methods for nonlinear equality constrained optizization without a penalty function [J].  Math.  Program.,  2003, 95: 103-135.
Schittkowski K. More test examples for nonlinear programming codes [M]. Springer-Verlag, 1987.
Options
Outlines

/

〈 〉