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.
fields
math.OC 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
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Primal-dual splitting for structured composite monotone inclusions with or without cocoercivity
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.