Differential systems for constrained optimization via a nonlinear augmented Lagrangian

A general differential system framework for solving constrained optimization problems is investigated, which relies on a class of nonlinear augmented Lagrangians. The differential systems mainly consist of first-order derivatives and second-order derivatives of the nonlinear augmented Lagrangian. Under suitable conditions, the asymptotic stability of the differential systems and local convergence properties of their Euler discrete schemes are obtained, including the locally quadratic convergence rate of the discrete sequence for the second-order derivatives based differential system. Furthermore, as the special case, the exponential Lagrangian applied to this framework is given. Numerical experiments are presented illustrating the performance of the differential systems.