The authors show how to swap exact proximal operators for Hamilton-Jacobi Monte Carlo estimates in five splitting algorithms and claim almost-sure convergence, with proof gaps that need repair.
The PGD iterates are computed by applying the mappingTk(x) = proxtkg(x−t k∇f(x))
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Operator Splitting with Hamilton-Jacobi-based Proximals
The authors show how to swap exact proximal operators for Hamilton-Jacobi Monte Carlo estimates in five splitting algorithms and claim almost-sure convergence, with proof gaps that need repair.