Interior-point augmented Lagrangian methods for constrained optimization

The interior-point approach is one kind of the most important and effective methods for nonlinear inequality-constrained optimization, whereas classic augmented Lagrangian methods are very efficient in solving nonlinear equality-constrained optimization and convex optimization. The new research has shown that the interior-point augmented Lagrangian function can be of very nice higher-order smoothness, and is convex when the original optimization problem is convex. These nice properties make the novel augmented Lagrangian applicable and effective not only for convex optimization but also for non-convex optimization problems. In this paper, we provide an overview of our recent research progress about the interior-point augmented Lagrange function methods on the non-convex and convex optimization, and point out prospects for future research directions.