Splitting Algorithm

Splitting algorithms are a class of optimization methods that decompose complex problems into smaller, more manageable subproblems, facilitating efficient solutions. Current research focuses on applying these algorithms to diverse fields, including image reconstruction (e.g., using half-quadratic splitting and Dykstra-like methods), solving partial differential equations (via variable splitting in Physics-Informed Neural Networks), and accelerating machine learning tasks (e.g., federated learning and diffusion models). The development and refinement of splitting algorithms significantly impact various scientific domains and practical applications by improving computational efficiency, enabling the solution of previously intractable problems, and enhancing the performance of machine learning models.