# Annealing for Distributed Global Optimization

## TL;DR

This paper introduces an annealing-based distributed algorithm for nonconvex optimization in multi-agent networks, proving convergence to global optima despite network variability and local nonconvexity.

## Contribution

It presents a novel consensus+innovations algorithm with annealing and noise decay, ensuring convergence to global minima in distributed nonconvex optimization.

## Key findings

- Convergence to global optima is proven under certain network and cost conditions.
- The algorithm achieves convergence in probability to the set of global minima.
- The approach handles time-varying communication graphs and local nonconvex functions.

## Abstract

The paper proves convergence to global optima for a class of distributed algorithms for nonconvex optimization in network-based multi-agent settings. Agents are permitted to communicate over a time-varying undirected graph. Each agent is assumed to possess a local objective function (assumed to be smooth, but possibly nonconvex). The paper considers algorithms for optimizing the sum function. A distributed algorithm of the consensus+innovations type is proposed which relies on first-order information at the agent level. Under appropriate conditions on network connectivity and the cost objective, convergence to the set of global optima is achieved by an annealing-type approach, with decaying Gaussian noise independently added into each agent's update step. It is shown that the proposed algorithm converges in probability to the set of global minima of the sum function.