Proximal Splitting

Proximal splitting methods are a class of algorithms used to solve complex optimization problems by decomposing them into simpler subproblems. Current research focuses on improving convergence speed through techniques like learning the underlying metric space and developing variants like Dykstra-like splitting and primal-dual proximal splitting algorithms, often tailored for specific applications such as image reconstruction and distributed optimization. These advancements are significant because they enable efficient solutions to large-scale problems across diverse fields, including machine learning, medical imaging, and game theory, where traditional methods struggle.