Gradient Sampling Methods

Abstract

One of the newest approaches in general nonsmooth optimization is to use gradient sampling algorithms developed by Burke, Lewis, and Overton. The gradient sampling method is a method for minimizing an objective function that is locally Lipschitz continuous and smooth on an open dense subset of \(\mathbb {R}^n\). The objective may be nonsmooth and/or nonconvex. Gradient sampling methods may be considered as a stabilized steepest descent algorithm. The central idea behind these techniques is to approximate the subdifferential of the objective function through random sampling of gradients near the current iteration point. In this chapter, we introduce the original gradient sampling algorithm.