CONVERGENCE PROPERTIES OF AN AUGMENTED LAGRANGIAN ALGORITHM FOR OPTIMIZATION WITH A COMBINATION OF GENERAL EQUALITY AND LINEAR CONSTRAINTS

We consider the global and local convergence properties of a class of augmented Lagrangian methods for solving nonlinear programming problem s. In these methods, linear and more general constraints are handled i n different ways. The general constraints are combined with the object ive function in an augmented Lagrangian. The iteration consists of sol ving a sequence of subproblems; in each subproblem the augmented Lagra ngian is approximately minimized in the region defined by the linear: constraints. A subproblem is terminated as soon as a stopping conditio n is satisfied, The stopping rules that we consider here encompass pra ctical tests used in several existing packages for linearly constraine d optimization. Our algorithm also allows different penalty parameters to be associated with disjoint subsets of the general constraints. In this paper, we analyze the convergence of the sequence of iterates ge nerated bg such an algorithm and prove global and fast linear converge nce as well as show that potentially troublesome penalty parameters re main bounded away from zero.