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

We consider the local convergence properties of the class of augmented Lagrangian methods for solving nonlinear programming problems whose global convergence properties are analyzed by Conn et al. (1993a). In these methods, linear constraints are treated separately from more general constraints. These latter constraints are combined with the objective function in an augmented Lagrangian while the subproblem then consists of (approximately) minimizing this augmented Lagrangian subject to the linear constraints. The stopping rule that we consider for the inner iteration covers practical tests used in several existing packages for linearly constrained optimization. Our algorithmic class allows several distinct penalty parameters to be associated with di erent subsets of general equality constraints. In this paper, we analyze the local convergence of the sequence of iterates generated by this technique and prove fast linear convergence and boundedness of the potentially troublesome 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)