# A Primal-Dual Quasi-Newton Method for Exact Consensus Optimization

arXiv: https://arxiv.org/abs/1809.01212 · HTML: https://mlsanity.com/paper/1809.01212/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2018.

## Built on by (most cited first, 2 of 2)

- [Data-driven Design of Context-aware Monitors for Hazard Prediction in Artificial Pancreas Systems](https://mlsanity.com/paper/2104.02545/) (2021)
- [CoCoL: A Communication Efficient Decentralized Collaborative Method for Multi-Robot Systems](https://mlsanity.com/paper/2508.20898/) (2025)

## Abstract (arXiv)

We introduce the primal-dual quasi-Newton (PD-QN) method as an approximated second order method for solving decentralized optimization problems. The PD-QN method performs quasi-Newton updates on both the primal and dual variables of the consensus optimization problem to find the optimal point of the augmented Lagrangian. By optimizing the augmented Lagrangian, the PD-QN method is able to find the exact solution to the consensus problem with a linear rate of convergence. We derive fully decentralized quasi-Newton updates that approximate second order information to reduce the computational burden relative to dual methods and to make the method more robust in ill-conditioned problems relative to first order methods. The linear convergence rate of PD-QN is established formally and strong performance advantages relative to existing dual and primal-dual methods are shown numerically.