A note on the convergence of deterministic gradient sampling in nonsmooth optimization
本文针对非光滑优化问题，提出一种结合二分法的确定性梯度采样方法，能在下降方向不足时计算新的次梯度，从而改进次微分逼近并保证收敛。
Abstract Approximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute new subgradients that improve a given approximation in case a direction with insufficient descent was computed. Combined with a recently proposed deterministic gradient sampling approach, this yields a deterministic and provably convergent way to approximate subdifferentials for computing descent directions.