Finite-Time Analysis of Stochastic Nonconvex Nonsmooth Optimization on the Riemannian Manifolds

A recent study has made significant strides in the field of nonsmooth nonconvex stochastic optimization by introducing a new algorithm called Riemannian Online to NonConvex (RO2NC). This research is important as it adapts the concept of Goldstein stationarity to Riemannian manifolds, providing a fresh performance metric for optimization in complex settings. The findings, which establish a sample complexity of O(ε⁻³δ⁻¹), could enhance the efficiency of optimization processes in various applications, making it a noteworthy advancement in mathematical optimization.