A Continuous Dynamical Newton-Like Approach to Solving Monotone Inclusions
SIAM Journal on Control and Optimization
Computational Optimization and Applications
Fixed Points of Averages of Resolvents: Geometry and Algorithms
SIAM Journal on Optimization
A Monotone+Skew Splitting Model for Composite Monotone Inclusions in Duality
SIAM Journal on Optimization
SIAM Journal on Optimization
A splitting algorithm for dual monotone inclusions involving cocoercive operators
Advances in Computational Mathematics
A proximal parallel splitting method for minimizing sum of convex functions with linear constraints
Journal of Computational and Applied Mathematics
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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.