Global convergence is proved. A computer implementation is fully described and a numerical comparison assesses the reliability of the new algorithm. A practical problem that requires the classification of a set of points of R n using a criterion not sensitive to outliers is studied in this paper. A fixed-point algorithm is defined that uses an arbitrary distance function.
Finite convergence is proved.
A robust distance defined by Boente, Fraiman and Yohai is selected for applications. Smooth approximations of this distance are defined and suitable heuristics are introduced to enhance the probability of finding global optimizers. A real-life example is presented and commented. Nonlinear programming, heuristics, clustering, classification, fixed points. Unfortunately, the nonnewtonian directions cease to be descent directions of the merit function.