Volume 22, Issue 5
A QP Free Feasible Method

Ding-guo Pu, Yan Zhou & Hai-yan Zhang

DOI:

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

Published online: 2004-10

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  • Abstract

In [12], a QP free feasible method was proposed for the minimization of a smooth func- tion 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 con- vergent 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.

  • Keywords

Constrained optimization KKT point Multiplier Nonlinear complementarity Convergence

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@Article{JCM-22-651, author = {}, 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 func- tion 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 con- vergent 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 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 KW - KKT point KW - Multiplier KW - Nonlinear complementarity KW - Convergence AB - In [12], a QP free feasible method was proposed for the minimization of a smooth func- tion 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 con- vergent 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.
Ding-guo Pu, Yan Zhou & Hai-yan Zhang . (1970). A QP Free Feasible Method. Journal of Computational Mathematics. 22 (5). 651-660. doi:
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