# Primal-Dual Algorithm for Distributed Constrained Optimization

arXiv: https://arxiv.org/abs/1510.08580 · HTML: https://mlsanity.com/paper/1510.08580/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2015.

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

- [Natural Policy Gradient and Actor Critic Methods for Constrained Multi-Task Reinforcement Learning](https://mlsanity.com/paper/2405.02456/) (2024)

## Abstract (arXiv)

The paper studies a distributed constrained optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local constraint sets assigned to the agents. Based on the augmented Lagrange method, a distributed primal-dual algorithm with a projection operation included is proposed to solve the problem. It is shown that with appropriately chosen constant step size, the local estimates derived at all agents asymptotically reach a consensus at an optimal solution. In addition, the value of the cost function at the time-averaged estimate converges with rate O(frac1k) to the optimal value for the unconstrained problem. By these properties the proposed primal-dual algorithm is distinguished from the existing algorithms for distributed constrained optimization. The theoretical analysis is justified by numerical simulations.