Volume 38, Issue 5
A Multidimensional Filter SQP Algorithm for Nonlinear Programming

Wenjuan Xue & Weiai Liu

J. Comp. Math., 38 (2020), pp. 683-704.

Published online: 2020-04

Preview Purchase PDF 13 3392
Export citation
  • Abstract

We propose a multidimensional filter SQP algorithm. The multidimensional filter technique proposed by Gould et al. [SIAM J. Optim., 2005] is extended to solve constrained optimization problems. In our proposed algorithm, the constraints are partitioned into several parts, and the entry of our filter consists of these different parts. Not only the criteria for accepting a trial step would be relaxed, but the individual behavior of each part of constraints is considered. One feature is that the undesirable link between the objective function and the constraint violation in the filter acceptance criteria disappears. The other is that feasibility restoration phases are unnecessary because a consistent quadratic programming subproblem is used. We prove that our algorithm is globally convergent to KKT points under the constant positive generators (CPG) condition which is weaker than the well-known Mangasarian-Fromovitz constraint qualification (MFCQ) and the constant positive linear dependence (CPLD). Numerical results are presented to show the efficiency of the algorithm.

  • Keywords

Trust region, Multidimensional filter, Constant positive generators, Global convergence, Nonlinear programming.

  • AMS Subject Headings

90C30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xuewenjuan@shiep.edu.cn (Wenjuan Xue)

weiailiu168@163.com (Weiai Liu)

  • BibTex
  • RIS
  • TXT
@Article{JCM-38-683, author = {Xue , Wenjuan and Liu , Weiai }, title = {A Multidimensional Filter SQP Algorithm for Nonlinear Programming}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {5}, pages = {683--704}, abstract = {

We propose a multidimensional filter SQP algorithm. The multidimensional filter technique proposed by Gould et al. [SIAM J. Optim., 2005] is extended to solve constrained optimization problems. In our proposed algorithm, the constraints are partitioned into several parts, and the entry of our filter consists of these different parts. Not only the criteria for accepting a trial step would be relaxed, but the individual behavior of each part of constraints is considered. One feature is that the undesirable link between the objective function and the constraint violation in the filter acceptance criteria disappears. The other is that feasibility restoration phases are unnecessary because a consistent quadratic programming subproblem is used. We prove that our algorithm is globally convergent to KKT points under the constant positive generators (CPG) condition which is weaker than the well-known Mangasarian-Fromovitz constraint qualification (MFCQ) and the constant positive linear dependence (CPLD). Numerical results are presented to show the efficiency of the algorithm.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1903-m2018-0072}, url = {http://global-sci.org/intro/article_detail/jcm/16664.html} }
TY - JOUR T1 - A Multidimensional Filter SQP Algorithm for Nonlinear Programming AU - Xue , Wenjuan AU - Liu , Weiai JO - Journal of Computational Mathematics VL - 5 SP - 683 EP - 704 PY - 2020 DA - 2020/04 SN - 38 DO - http://doi.org/10.4208/jcm.1903-m2018-0072 UR - https://global-sci.org/intro/article_detail/jcm/16664.html KW - Trust region, Multidimensional filter, Constant positive generators, Global convergence, Nonlinear programming. AB -

We propose a multidimensional filter SQP algorithm. The multidimensional filter technique proposed by Gould et al. [SIAM J. Optim., 2005] is extended to solve constrained optimization problems. In our proposed algorithm, the constraints are partitioned into several parts, and the entry of our filter consists of these different parts. Not only the criteria for accepting a trial step would be relaxed, but the individual behavior of each part of constraints is considered. One feature is that the undesirable link between the objective function and the constraint violation in the filter acceptance criteria disappears. The other is that feasibility restoration phases are unnecessary because a consistent quadratic programming subproblem is used. We prove that our algorithm is globally convergent to KKT points under the constant positive generators (CPG) condition which is weaker than the well-known Mangasarian-Fromovitz constraint qualification (MFCQ) and the constant positive linear dependence (CPLD). Numerical results are presented to show the efficiency of the algorithm.

Wenjuan Xue & Weiai Liu. (2020). A Multidimensional Filter SQP Algorithm for Nonlinear Programming. Journal of Computational Mathematics. 38 (5). 683-704. doi:10.4208/jcm.1903-m2018-0072
Copy to clipboard
The citation has been copied to your clipboard