Newton's method for singular constrained optimization problems

We consider an iterative procedure where at each iteration a constrained quadratic optimization problem is solved. A Goldstein type step length rule is incorporated in order to assure global convergence. We consider a class of minimization problems which are singular at the optimal point and show that locally the superlinear convergence rate is retained for a certain part of the iterations. These results are applied to problems with perturbed data. In the last section global convergence results are proven.