Convergence Properties of an Augmentedlagrangian Algorithm for Optimization with Acombination

We consider the global and local convergence properties of a class of augmented La-grangian methods for solving nonlinear programming problems. In these methods, linear and more general constraints are handled in diierent ways. The general constraints are combined with the objective function in an augmented Lagrangian. The iteration consists of solving a sequence of sub-problems; in each subproblem the augmented Lagrangian is approximately minimized in the region deened by the linear constraints. A subproblem is terminated as soon as a stopping condition is satissed. The stopping rules that we consider here encompass practical tests used in several existing packages for linearly constrained optimization. Our algorithm also allows diierent penalty parameters to be associated with disjoint subsets of the general constraints. In this paper, we analyze the convergence of the sequence of iterates generated by such an algorithm and prove global and fast linear convergence as well as showing that potentially troublesome penalty parameters remain bounded away from zero.