Convergence analysis of the augmented Lagrangian method for ℓp-norm cone optimization problems with p ≥ 2

This paper focuses on the convergence analysis of the augmented Lagrangian method (ALM) for & ell;(p)-norm cone optimization problems. We investigate some properties of the augmented Lagrangian function and & ell;(p)-norm cone. Moreover, under the Jacobian uniqueness conditions, we prove that the local convergence rate of ALM for solving & ell;(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.