Proximal Point Algorithm

The proximal point algorithm (PPA) is an iterative optimization method that solves complex problems by repeatedly solving simpler subproblems. Current research focuses on improving PPA's efficiency and robustness, particularly through preconditioning techniques, stabilized variants (like S-DANE), and adaptations for distributed and quantum computing environments. These advancements address limitations such as slow convergence in high-dimensional spaces and communication bottlenecks in federated learning, enhancing PPA's applicability to diverse fields like image processing and machine learning. The resulting improvements in speed and scalability significantly impact the feasibility of solving large-scale optimization problems across various scientific and engineering domains.