A Globally Convergent Lagrangian Barrier Algorithm for Optimization with General Inequality Constraints

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 Lagrangian barrier functions are approximately minimized within the domain de ned by the simple bounds. Global convergence of the sequence of generated iterates to a rst-order stationary point for the original problem is established. Furthermore, possible numerical di culties 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 (see, Conn et al., 1991) on augmented Lagrangian methods. 1 Mathematical Sciences Department, IBM T.J. Watson Research Center, PO Box 218, Yorktown Heights, NY 10598, USA 2 Central Computing Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, England 3 Department of Mathematics, Facult es Universitaires ND de la Paix, B-5000 Namur, Belgium