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

arXiv: https://arxiv.org/abs/2302.13128 · HTML: https://mlsanity.com/paper/2302.13128/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2023.

## Built on by (most cited first, 1 of 1)

- [Learning Over-Relaxation Policies for ADMM with Convergence Guarantees](https://mlsanity.com/paper/2604.26932/) (2026)

## Abstract (arXiv)

In this paper the degenerate preconditioned proximal point algorithm will be combined with the idea of varying preconditioners leading to the degenerate variable metric proximal point algorithm. The weak convergence of the resulting iteration will be proven. From the perspective of the degenerate variable metric proximal point algorithm, a version of the primal-dual Douglas-Rachford method with varying preconditioners will be derived and a proof of its weak convergence which is based on the previous results for the proximal point algorithm, is provided, too. After that, we derive a heuristic on how to choose those varying preconditioners in order to increase the convergence speed of the method.