arrow
Volume 22, Issue 5
A QP Free Feasible Method

Dingguo Pu, Yan Zhou & Haiyan Zhang

J. Comp. Math., 22 (2004), pp. 651-660.

Published online: 2004-10

Export citation
  • Abstract

In [12], a QP free feasible method was proposed for the minimization of a smooth function subject to smooth inequality constraints. This method is based on the solutions of linear systems of equations, the reformulation of the KKT optimality conditions by using the Fischer-Burmeister NCP function. This method ensures the feasibility of all iterations. In this paper, we modify the method in [12] slightly to obtain the local convergence under some weaker conditions. In particular, this method is implementable and globally convergent without assuming the linear independence of the gradients of active constrained functions and the uniformly positive definiteness of the submatrix obtained by the Newton or Quasi Newton methods. We also prove that the method has superlinear convergence rate under some mild conditions. Some preliminary numerical results indicate that this new QP free feasible method is quite promising.  

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{JCM-22-651, author = {Pu , DingguoZhou , Yan and Zhang , Haiyan}, title = {A QP Free Feasible Method}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {5}, pages = {651--660}, abstract = {

In [12], a QP free feasible method was proposed for the minimization of a smooth function subject to smooth inequality constraints. This method is based on the solutions of linear systems of equations, the reformulation of the KKT optimality conditions by using the Fischer-Burmeister NCP function. This method ensures the feasibility of all iterations. In this paper, we modify the method in [12] slightly to obtain the local convergence under some weaker conditions. In particular, this method is implementable and globally convergent without assuming the linear independence of the gradients of active constrained functions and the uniformly positive definiteness of the submatrix obtained by the Newton or Quasi Newton methods. We also prove that the method has superlinear convergence rate under some mild conditions. Some preliminary numerical results indicate that this new QP free feasible method is quite promising.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8864.html} }
TY - JOUR T1 - A QP Free Feasible Method AU - Pu , Dingguo AU - Zhou , Yan AU - Zhang , Haiyan JO - Journal of Computational Mathematics VL - 5 SP - 651 EP - 660 PY - 2004 DA - 2004/10 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8864.html KW - Constrained optimization, KKT point, Multiplier, Nonlinear complementarity, Convergence. AB -

In [12], a QP free feasible method was proposed for the minimization of a smooth function subject to smooth inequality constraints. This method is based on the solutions of linear systems of equations, the reformulation of the KKT optimality conditions by using the Fischer-Burmeister NCP function. This method ensures the feasibility of all iterations. In this paper, we modify the method in [12] slightly to obtain the local convergence under some weaker conditions. In particular, this method is implementable and globally convergent without assuming the linear independence of the gradients of active constrained functions and the uniformly positive definiteness of the submatrix obtained by the Newton or Quasi Newton methods. We also prove that the method has superlinear convergence rate under some mild conditions. Some preliminary numerical results indicate that this new QP free feasible method is quite promising.  

Dingguo Pu, Yan Zhou & Haiyan Zhang. (1970). A QP Free Feasible Method. Journal of Computational Mathematics. 22 (5). 651-660. doi:
Copy to clipboard
The citation has been copied to your clipboard