Global Convergence of two Augmented Lagrangian Algorithms for Optimization with a Combination of General Equality and Linear Constraints

We consider the global convergence properties of a class of augmented Lagrangian methods for solving nonlinear programming problems. In the proposed method, linear constraints are treated separately from more general constraints. Thus only the latter are combined with the objective function in an augmented Lagrangian. The subproblem then consists of (approximately) minimizing this augmented Lagrangian subject to the linear constraints. In this paper, we prove the global convergence of the sequence of iterates generated by this technique to a rst-order stationary point of the original problem. We consider various stopping rules for the iterative solution of the subproblem, including practical tests used in several existing packages for linearly constrained optimization. We also extend our results to the case where the augmented Lagrangian's de nition involves several distinct penalty parameters. 1 IBM T.J. Watson Research Center, P.O.Box 218, Yorktown Heights, NY 10598, USA Email : [email protected] 2 CERFACS, 42 Avenue Gustave Coriolis, 31057 Toulouse Cedex, France, EC Email : [email protected] or [email protected] Current reports available by anonymous ftp from the directory \pub/reports" on camelot.cc.rl.ac.uk (internet 130.246.8.61) 3 Department of Mathematics, Facult es Universitaires ND de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium, EC Email : [email protected] or [email protected] Current reports available by anonymous ftp from the directory \reports" on thales.math.fundp.ac.be (internet 138.48.4.14)