Superlinear and quadratic convergence of affine-scaling interior-point Newton methods for problems with simple bounds without strict complementarity assumption

A class of affine-scaling interior-point methods for bound constrained opti mization problems is introduced which are locally q-superlinear or q-quadra tic convergent. It is assumed that the strong second order sufficient optim ality conditions at the solution are satisfied, hut strict complementarity is not required. The methods are modifications of the affine-scaling interi or-point Newton methods introduced by T. F. Coleman and Y. Li (Math. Progra mming, 67, 189-224, 1994). There are two modifications. One is a modificati on of the scaling matrix, the other one is the use of a projection of the s tep to maintain strict feasibility rather than a simple scaling of the step . A comprehensive local convergence analysis is given. A simple example is presented to illustrate the pitfalls of the original approach by Coleman an d Li in the degenerate case and to demonstrate the performance of the fast converging modifications developed in this paper.