# A distributed semismooth Newton based augmented Lagrangian method for distributed optimization

arXiv: https://arxiv.org/abs/2602.23854 · HTML: https://mlsanity.com/paper/2602.23854/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 33 references that are in the map.
- First posted on arXiv 27 Feb 2026.

## Builds on (most cited first, 8 of 8)

- [EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization](https://mlsanity.com/paper/1404.6264/) (2014)
- [Achieving Geometric Convergence for Distributed Optimization over Time-Varying Graphs](https://mlsanity.com/paper/1607.03218/) (2016)
- [A Dual Approach for Optimal Algorithms in Distributed Optimization over Networks](https://mlsanity.com/paper/1809.00710/) (2018)
- [Accelerated Distributed Nesterov Gradient Descent](https://mlsanity.com/paper/1705.07176/) (2017)
- [Distributed Algorithms for Composite Optimization: Unified Framework and Convergence Analysis](https://mlsanity.com/paper/2002.11534/) (2020)
- [Distributed Proximal Gradient Algorithm for Partially Asynchronous Computer Clusters](https://mlsanity.com/paper/1704.03540/) (2017)
- [Distributed Adaptive Newton Methods with Global Superlinear Convergence](https://mlsanity.com/paper/2002.07378/) (2020)
- [On Distributed Nonconvex Optimisation Via Modified ADMM](https://mlsanity.com/paper/2312.03958/) (2023)

## Abstract (arXiv)

This paper proposes a novel distributed semismooth Newton based augmented Lagrangian method for solving a class of optimization problems over networks, where the global objective is defined as the sum of locally held cost functions, and communication is restricted to neighboring agents. Specifically, we employ the augmented Lagrangian method to solve an equivalently reformulated constrained version of the original problem. Each resulting subproblem is solved inexactly via a distributed semismooth Newton method. By fully leveraging the structure of the generalized Hessian, a distributed accelerated proximal gradient method is proposed to compute the Newton direction efficiently, eliminating the need to communicate with full Hessian matrices. Theoretical results are also obtained to guarantee the convergence of the proposed algorithm. Numerical experiments demonstrate the efficiency and superiority of our algorithm compared to state-of-the-art distributed algorithms.