# A randomized primal distributed algorithm for partitioned and big-data non-convex optimization

## TL;DR

This paper introduces a simple, randomized primal distributed algorithm for large-scale, partitioned, non-convex optimization problems in network settings, demonstrating convergence and effectiveness through theoretical analysis and simulations.

## Contribution

It proposes a novel asynchronous, randomized primal algorithm for distributed non-convex optimization that converges to stationary points, suitable for big-data network applications.

## Key findings

- Algorithm converges to stationary points in non-convex settings.
- Effective in asynchronous gossip communication environments.
- Numerical simulations confirm theoretical convergence results.

## Abstract

In this paper we consider a distributed optimization scenario in which the aggregate objective function to minimize is partitioned, big-data and possibly non-convex. Specifically, we focus on a set-up in which the dimension of the decision variable depends on the network size as well as the number of local functions, but each local function handled by a node depends only on a (small) portion of the entire optimization variable. This problem set-up has been shown to appear in many interesting network application scenarios. As main paper contribution, we develop a simple, primal distributed algorithm to solve the optimization problem, based on a randomized descent approach, which works under asynchronous gossip communication. We prove that the proposed asynchronous algorithm is a proper, ad-hoc version of a coordinate descent method and thus converges to a stationary point. To show the effectiveness of the proposed algorithm, we also present numerical simulations on a non-convex quadratic program, which confirm the theoretical results.