A Globally Convergent Lagrangian Barrier Algorithm
for Optimization with General Inequality Constraints
and Simple Bounds
A.R. Conn, Nick Gould and Ph.L. Toint
Report 92/07
We consider the global and local convergence
properties of a class of Lagrangian barrier methods
for solving nonlinear programming problems. In such
methods, simple bound constraints may be treated
separately from more general constraints. The
objective and general constraint functions are
combined in a Lagrangian barrier function. A sequence
of such functions are approximately minimized within
the domain defined by the simple bounds. Global
convergence of the sequence of generated iterates to a
first-order stationary point for the original problem
is established. Furthermore, possible numerical
difficulties associated with barrier function methods
are avoided as it is shown that a potentially
troublesome penalty parameter is bounded away from
zero. This paper is a companion to our previous work
on augmented Lagrangian methods.