# Towards Parameter-free Distributed Optimization: a Port-Hamiltonian Approach

arXiv: https://arxiv.org/abs/2404.13529 · HTML: https://mlsanity.com/paper/2404.13529/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Apr 2024.

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

- [Adaptive Decentralized Composite Optimization via Three-Operator Splitting](https://mlsanity.com/paper/2602.17545/) (2026)

## Abstract (arXiv)

This paper introduces a novel distributed optimization technique for networked systems, which removes the dependency on specific parameter choices, notably the learning rate. Traditional parameter selection strategies in distributed optimization often lead to conservative performance, characterized by slow convergence or even divergence if parameters are not properly chosen. In this work, we propose a systems theory tool based on the port-Hamiltonian formalism to design algorithms for consensus optimization programs. Moreover, we propose the Mixed Implicit Discretization (MID), which transforms the continuous-time port-Hamiltonian system into a discrete time one, maintaining the same convergence properties regardless of the step size parameter. The consensus optimization algorithm enhances the convergence speed without worrying about the relationship between parameters and stability. Numerical experiments demonstrate the method's superior performance in convergence speed, outperforming other methods, especially in scenarios where conventional methods fail due to step size parameter limitations.