The global convergence of augmented Lagrangian methods based on NCP function in constrained nonconvex optimization
The authors study the global convergence properties for modified augmented Lagrangian methods using a class of augmented Lagrangian functions based on nonlinear complementarity problem (NCP) function for inequality constrained optimization problems. They show that under weaker conditions, the augmented Lagrangian method using safeguarding strategy converges to a Karush-Kuhn-Tucker point or a degenerate point of the original problem. The convergence properties of the augmented Lagrangian method using conditional multiplier updating rule is presented. The use of penalty parameter updating criteria and normalization of the multipliers in augmented Lagrangian methods is investigated. Some preliminary numerical results on the four proposed modified augmented algorithms are presented.
scientific article; zbMATH DE number 5522196
scientific article