New Convergence Properties of the Primal Augmented Lagrangian Method

Abstract EN

New convergence properties of the proximal augmented Lagrangian method is established for continuous nonconvex optimization problem with both equality and inequality constrains.

In particular, the multiplier sequences are not required to be bounded.

Different convergence results are discussed dependent on whether the iterative sequence {xk} generated by algorithm is convergent or divergent.

Furthermore, under certain convexity assumption, we show that every accumulation point of {xk} is either a degenerate point or a KKT point of the primal problem.

Numerical experiments are presented finally.