# Distributed constrained optimization and consensus in uncertain networks via proximal minimization

arXiv: https://arxiv.org/abs/1603.02239 · HTML: https://mlsanity.com/paper/1603.02239/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Mar 2016.

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

- [Compression, Generalization and Learning](https://mlsanity.com/paper/2301.12767/) (2023)
- [A One-Sample Decentralized Proximal Algorithm for Non-Convex Stochastic Composite Optimization](https://mlsanity.com/paper/2302.09766/) (2023)

## Abstract (arXiv)

We provide a unifying framework for distributed convex optimization over time-varying networks, in the presence of constraints and uncertainty, features that are typically treated separately in the literature. We adopt a proximal minimization perspective and show that this set-up allows us to bypass the difficulties of existing algorithms while simplifying the underlying mathematical analysis. We develop an iterative algorithm and show convergence of the resulting scheme to some optimizer of the centralized problem. To deal with the case where the agents' constraint sets are affected by a possibly common uncertainty vector, we follow a scenario-based methodology and offer probabilistic guarantees regarding the feasibility properties of the resulting solution. To this end, we provide a distributed implementation of the scenario approach, allowing agents to use a different set of uncertainty scenarios in their local optimization programs. The efficacy of our algorithm is demonstrated by means of a numerical example related to a regression problem subject to regularization.