Convergence analysis of the augmented Lagrangian method for ℓp-norm cone optimization problems with p≥2 - Liu, Benqi; Gong, Kai; Zhang, Liwei (Numerical algorithms, 2025)
This paper focuses on the convergence analysis of the augmented Lagrangian method (ALM) for ℓ p -norm cone optimization problems. We investigate some properties of the augmented Lagrangian function and ℓ p -norm cone. Moreover, under the Jacobian uniqueness conditions, we prove that the local convergence rate of ALM for solving ℓ p -norm cone optimization problems with p ≥ 2 is proportional to 1 / r , where the penalty parameter r is not less than a threshold r ^ . In numerical simulations, we successfully validate the effectiveness and convergence properties of ALM.