A nonsmooth nonconvex descent algorithm

Abstract

The paper presents a new descent algorithm for locally Lipschitz continuous functions $f:X\to \mathbb{R}$. The selection of a descent direction at some iteration point $x$ combines an approximation of the set-valued gradient of $f$ on a suitable neighborhood of $x$ (recently introduced by Mankau & Schuricht) with an Armijo type step control. The algorithm is analytically justified and it is shown that accumulation points of iteration points are critical points of $f$. Finally the algorithm is tested for numerous benchmark problems and the results are compared with simulations found in the literature.