An Example of Only Linear Convergence of Trust Region Algorithms for Non-smooth Optimization

Most superlinear convergence results about trust region algorithmsfor non-smooth optimization are dependent on the inactivityof trust region restrictions. An example is constructed to showthat it is possible that at every iteration the trust regionbound is active and the rate of convergence is only linear,though strict complementarity and second order sufficiency conditionsare satisfied. Presented at the 1983 Dundee Conference on Numerical Analysis