Theoretical analysis demonstrates strong convergence of splitting algorithms for state-dependent maximal monotone inclusions, highlighting performance gains over existing methods.
We consider the state-dependent maximal monotone inclusion problem and propose forward-backward splitting algorithms for solving it. Strong convergence of the proposed algorithms is established under suitable conditions. For the special separable case, we present an improved Douglas–Rachford variant that can be easily implemented. Moreover, some accelerated forward-backward splitting algorithms are also presented. Preliminary numerical experiments with comparisons to existing results are presented, illustrating the advantages of our methods.
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Li et al. (2024) studied this question.
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