Approximating Clarke's subgradients of semismooth functions by divided differences (Q877273)

The aim of this paper is to demonstrate that the algorithm proposed by \textit{M. Studniarski} [Numer. Math. 55, 685--693 (1989; Zbl 0671.65044)] can be extended to a more general class of nonsmooth functions. That class is the one of semismooth functions introduced by \textit{R. Mifflin} [SIAM J. Control Optim. 15, 959--972 (1977; Zbl 0376.90081)]. A semismooth function has generalized gradients in the sense of Clarke and one-sided directional derivatives in every direction. The algorithm in the present paper works only for functions of two variables. Its convergence is demonstrated and some numerical tests are presented.