A Globally Convergent Penalty-Barrier Algorithm for Nonlinear Programming

The global convergence properties of a penalty-barrier method for solving equality and/or inequality constrained nonlinear optimization problems are considered. The presented algorithm is a composite of augmented Lagrangian, modified log-barrier, and classical log-barrier methods. Under common conditions, global convergence of a sequence of iterates to a first-order stationary point for the constrained problem is established. The iterates are approximate minima of a sequence of unconstrained penalty-barrier functions. Extensive computational tests suggest that the presented penalty-barrier algorithm is a robust and efficient method for solving general nonlinear optimization problems.