# Distributed Adaptive Gradient Optimization Algorithm

## TL;DR

This paper introduces two distributed adaptive gradient algorithms for multi-agent systems to optimize convex functions, demonstrating convergence through Lyapunov analysis and numerical validation.

## Contribution

It presents novel adaptive algorithms that utilize relative information to enhance distributed convex optimization in multi-agent systems.

## Key findings

- Algorithms successfully minimize convex objectives over time.
- Convergence proven using Lyapunov functions and system analysis.
- Numerical examples validate theoretical results.

## Abstract

In this paper, a distributed optimization problem with general differentiable convex objective functions is studied for single-integrator and double-integrator multi-agent systems. Two distributed adaptive optimization algorithm is introduced which uses the relative information to construct the gain of the interaction term. The analysis is performed based on the Lyapunov functions, the analysis of the system solution and the convexity of the local objective functions. It is shown that if the gradients of the convex objective functions are continuous, the team convex objective function can be minimized as time evolves for both single-integrator and double-integrator multi-agent systems. Numerical examples are included to show the obtained theoretical results.