A new primal-dual splitting algorithm unifies methods for monotone inclusions, handles non-cocoercive operators, reduces dimensionality, and allows larger stepsizes via a single convergence analysis.
A general approach to distributed operator splitting
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abstract
Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone inclusion problems involving both set-valued and single-valued operators, where the latter may lack cocoercivity. Our proposed approach, based on some coefficient matrices, not only encompasses several important existing algorithms but also extends to new ones, offering greater flexibility for different applications. Moreover, by appropriately selecting the coefficient matrices, the resulting algorithms can be implemented in a distributed and decentralized manner.
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A new primal-dual splitting method for structured monotone inclusions that generalizes prior algorithms, requires one resolvent evaluation per step, and proves weak convergence under monotonicity plus strong convergence under uniform monotonicity.
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A primal-dual splitting algorithm for monotone inclusions with applications
A new primal-dual splitting method for structured monotone inclusions that generalizes prior algorithms, requires one resolvent evaluation per step, and proves weak convergence under monotonicity plus strong convergence under uniform monotonicity.