Improved local convergence results for augmented Lagrangian methods in \(C^2\)-cone reducible constrained optimization (Q2316626)

This paper considers the local convergence of the augmented Lagrangian method for generic \(C^2\)-cone reducible problems, thereby subsuming semidefinite and second-order cone programming. It is proved that the augmented Lagrangian method converges locally for \(C^2\)-cone reducible constrained optimization problems under the second-order sufficient condition and a strict version of the Robinson constraint qualification. This analysis does not require any assumptions on the initial multiplier estimate. Additionally, under the same assumptions, a primal-dual error bound on the KKT system is obtained which does not require any (a-priori) proximity of the multiplier to the optimal one.