Minimization of SC1 functions and the Maratos effect

The paper considers the unconstrained minimization of a continuously differentiable function with semismooth gradient by line search methods; in particular it focuses on the problem of the acceptance of the unit stepsize. The paper shows that, under mild conditions, if the full search direction brings superlinear convergence, then the unit stepsize is eventually accepted so that the Maratos effect does not occur. The relevance to this issue of a generalization of the classical second-order sufficient condition for optimality is pointed out.