Mixed penalties: A two-step superlinear algorithm

In this paper, the authors present an extrapolation strategy to obtain good starting points for the unconstrained subproblems coming from a mixed penalty algorithm in general constrained nonlinear programming. This strategy allows to obtain the two-steps superlinear local convergence property. Also, the authors show that the usual ill-conditioning the plague most penalty algorithms may be removed using clever transformations of the Karush-Kuhn-Tucker equations.