Spurious Stationary Points and Hardness Results for Bregman Proximal-Type Algorithms

The existence of spurious stationary points, which satisfy the zero extended Bregman stationarity measure but are not true stationary points, poses fundamental challenges to the analysis and design of Bregman proximal-type algorithms. These spurious points can trap the algorithms within a small neighborhood, even for convex problems, highlighting the inherent distinction between Euclidean and Bregman geometries.