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In this paper the degenerate preconditioned proximal point algorithm will becombined with the idea of varying preconditioners leading to the degeneratevariable metric proximal point algorithm. The weak convergence of the resultingiteration will be proven. From the perspective of the degenerate variablemetric proximal point algorithm, a version of the primal-dual Douglas-Rachfordmethod with varying preconditioners will be derived and a proof of its weakconvergence which is based on the previous results for the proximal pointalgorithm, is provided, too. After that, we derive a heuristic on how to choosethose varying preconditioners in order to increase the convergence speed of themethod.

The Degenerate Variable Metric Proximal Point Algorithm and Adaptive Stepsizes for Primal-Dual Douglas-Rachford