Proximal Operator

Proximal operators are fundamental mathematical tools used to solve optimization problems, particularly those involving non-smooth or non-convex functions, by iteratively minimizing a regularized version of the objective function. Current research focuses on developing efficient algorithms for computing proximal operators, including neural network approximations and methods tailored to specific problem structures like unbalanced optimal transport and optimization on manifolds. These advancements are crucial for improving the efficiency and robustness of various applications, such as inverse problems in image processing, federated learning, and generative modeling, where the ability to efficiently handle complex objective functions is paramount.