# Gradient-Free Multi-Agent Nonconvex Nonsmooth Optimization

## TL;DR

This paper introduces a distributed gradient-free algorithm for multi-agent nonconvex, nonsmooth optimization, demonstrating convergence to stationary points with proven sublinear rates, suitable for scenarios with limited information access.

## Contribution

It presents a novel primal-dual gradient-free method for distributed nonconvex nonsmooth optimization with theoretical convergence guarantees.

## Key findings

- Algorithm converges to stationary solutions
- Achieves global sublinear convergence rate
- Effective in numerical experiments for complex problems

## Abstract

In this paper, we consider the problem of minimizing the sum of nonconvex and possibly nonsmooth functions over a connected multi-agent network, where the agents have partial knowledge about the global cost function and can only access the zeroth-order information (i.e., the functional values) of their local cost functions. We propose and analyze a distributed primal-dual gradient-free algorithm for this challenging problem. We show that by appropriately choosing the parameters, the proposed algorithm converges to the set of first order stationary solutions with a provable global sublinear convergence rate. Numerical experiments demonstrate the effectiveness of our proposed method for optimizing nonconvex and nonsmooth problems over a network.