H\"older Function

Hölder continuity, a generalization of Lipschitz continuity, describes functions whose rate of change is bounded by a power law. Current research focuses on leveraging this property in optimization algorithms, particularly for non-convex problems where traditional methods struggle, employing techniques like adaptive proximal gradient methods and Newton-CG methods. These advancements are improving the efficiency and convergence guarantees of optimization algorithms in machine learning and other fields where functions may lack smoothness. The broader impact lies in enabling more robust and efficient solutions for problems involving complex, potentially discontinuous, functions.