Dykstra's alternating projection algorithm for two sets
Journal of Approximation Theory
Parallel Optimization: Theory, Algorithms and Applications
Parallel Optimization: Theory, Algorithms and Applications
Proximal Point Approach and Approximation of Variational Inequalities
SIAM Journal on Control and Optimization
SIAM Journal on Optimization
Finding best approximation pairs relative to two closed convex sets in Hilbert spaces
Journal of Approximation Theory
A New Class of Alternating Proximal Minimization Algorithms with Costs-to-Move
SIAM Journal on Optimization
Hard-constrained inconsistent signal feasibility problems
IEEE Transactions on Signal Processing
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A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces, and its convergence is established under the assumption that solutions exist. Unlike existing alternating algorithms, which are limited to two variables and linear coupling, our parallel method can handle an arbitrary number of variables as well as nonlinear coupling schemes. The breadth and flexibility of the proposed framework is illustrated through applications in the areas of evolution inclusions, variational problems, best approximation, and network flows.