For nonconvex problems with equality and inequality constraints and a known feasible point, an inexact proximal augmented Lagrangian method with adaptive parameter updates reaches an epsilon-KKT point in finitely many iterations.
Constrained model predictive control: Stability and optimality.Automatica, 36(6):789–814, 2000
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A proximal augmented Lagrangian method for nonconvex optimization with equality and inequality constraints
For nonconvex problems with equality and inequality constraints and a known feasible point, an inexact proximal augmented Lagrangian method with adaptive parameter updates reaches an epsilon-KKT point in finitely many iterations.