This is much cheaper than the standard proximal operator with Euclidean distances, which requires an eigenvalue decomposition.

Proximal Algorithms discusses proximal operators and proximal algorithms, and illustrates their applicability to standard and distributed convex optimization in general and many applications of recent interest in particular.

This algorithm is computationally light, as it involves closed-form updates. This approach is demonstrated on a large wind farm with 60 turbines.

This book presents tools and methods for large-scale and distributed optimization.

This book comes close to bridging that gap, presenting a new framework for the theory of primal-dual IPMs based on the notion of the self-regularity of a function.

... proximal gradient algorithm for decentralized composite optimization. IEEE Trans. Signal Process. 63(22), 6013–6023 ... primal-dual strategy for composite opti- mization over distributed features, inProceedings of the 2020 28th ...

Surveys the theory and history of the alternating direction method of multipliers, and discusses its applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic ...

We introduce a primal-dual stochastic gradient oracle method for distributed convex optimization problems over networks.

... proximal gradient method for sparse nonnegative Tucker decomposition. Mathematical Programming Computation, 7(1):39–70, 2015. Y. Xu. Accelerated first-order primal-dual ... algorithm for nonconvex optimization based on block coordinate ...

... dual proximal gradient algorithms for non-smooth constrained composite optimization problems. IEEE Trans. Parallel Distrib. Syst. 32(10), 2594–2605 (2021) 2. Latafat, P., Freris, N.M., Patrinos, P.: A new randomized block-coordinate primal- ...