@Article{JCM-38-5,
author = {Xue, Wenjuan and Weiai, Liu},
title = {A Multidimensional Filter SQP Algorithm for Nonlinear Programming},
journal = {Journal of Computational Mathematics},
year = {2020},
volume = {38},
number = {5},
pages = {683--704},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1903-m2018-0072},
url = {https://global-sci.com/article/84348/a-multidimensional-filter-sqp-algorithm-for-nonlinear-programming}
}