Nonsmooth Dynamical System

Nonsmooth dynamical systems encompass a broad class of optimization problems characterized by objective functions lacking continuous derivatives, posing significant challenges for traditional optimization methods. Current research focuses on developing and analyzing algorithms like proximal gradient descent, stochastic approximation, and variants of the alternating direction method of multipliers (ADMM), often incorporating techniques such as randomized smoothing and block coordinate descent to handle the nonsmoothness efficiently. These advancements are crucial for addressing numerous applications in machine learning, signal processing, and control theory where nonsmoothness arises naturally, leading to improved efficiency and robustness in solving complex optimization problems. The development of user-friendly software packages further enhances accessibility and impact within the broader scientific community.