TY - JOUR
T1 - An Augmented Lagrangian Trust Region Method with a Bi-Object Strategy
AU - Kou , Caixia
AU - Chen , Zhongwen
AU - Dai , Yuhong
AU - Han , Haifei
JO - Journal of Computational Mathematics
VL - 3
SP - 331
EP - 350
PY - 2018
DA - 2018/06
SN - 36
DO - http://doi.org/10.4208/jcm.1705-m2016-0820
UR - https://global-sci.org/intro/article_detail/jcm/12264.html
KW - Nonlinear constrained optimization, Augmented Lagrangian function, Bi-object strategy, Global convergence.
AB - <p style="text-align: justify;">An augmented Lagrangian trust region method with a bi-object strategy is proposed for
solving nonlinear equality constrained optimization, which falls in between penalty-type
methods and penalty-free ones. At each iteration, a trial step is computed by minimizing
a quadratic approximation model to the augmented Lagrangian function within a trust
region. The model is a standard trust region subproblem for unconstrained optimization
and hence can efficiently be solved by many existing methods. To choose the penalty
parameter, an auxiliary trust region subproblem is introduced related to the constraint
violation. It turns out that the penalty parameter need not be monotonically increasing
and will not tend to infinity. A bi-object strategy, which is related to the objective function
and the measure of constraint violation, is utilized to decide whether the trial step will be
accepted or not. Global convergence of the method is established under mild assumptions.
Numerical experiments are made, which illustrate the efficiency of the algorithm on various
difficult situations.</p>