MINIMIZATION OF SC1 FUNCTIONS AND THE MARATOS EFFECT

We consider the unconstrained minimization of a continuously different iable function with semismooth gradient by line search methods; in par ticular we focus on the problem of the acceptance of the unit stepsize . We show that, under mild conditions, if the full search direction br ings superlinear convergence, then the unit stepsize is eventually acc epted so that: the Maratos effect does not occur. The relevance to thi s issue of a generalization of the classical second-order sufficient c ondition for optimality is pointed out.