The relocated fixed-point iteration framework proves weak convergence of variable-stepsize Douglas-Rachford and resolvent splitting methods without requiring a common fixed point.
Bhatia.Perturbation Bounds for Matrix Eigenvalues
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Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting
The relocated fixed-point iteration framework proves weak convergence of variable-stepsize Douglas-Rachford and resolvent splitting methods without requiring a common fixed point.