Local Convergence Properties of two Augmented
Lagrangian Algorithms for Optimization
with a Combination of General Equality
and Linear Constraints
A.R. Conn, Nick Gould,
A. Sartenaer and Ph.L. Toint
Abstract. 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.
(1993). 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
different 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.