LOCAL AND GLOBAL ANALYSIS OF MULTIPLIER METHODS FOR CONSTRAINED OPTIMIZATION IN BANACH SPACES

We propose an augmented Lagrangian method for the solution of constrained optimization problems in Banach spaces. The framework we consider is very general and encompasses a host of standard problems such as nonlinear programming, semidefinite programming, and optimal control. We analyze several convergence-related aspects of the method, including global convergence, the attainment of feasibility, and local convergence. In particular, a result is presented which guarantees local convergence of the method under the sole assumption that a solution of the problem satisfies the second-order sufficient condition. Finally, we give detailed numerical results for optimal control problems and mathematical programs with complementarity constraints.