# Totally Asynchronous Distributed Quadratic Programming with Independent Stepsizes and Regularizations

## TL;DR

This paper introduces a flexible multi-agent framework for large-scale quadratic programming that allows asynchronous updates, independent parameter choices, and regularizations, ensuring convergence without strict timing or coupling constraints.

## Contribution

It presents a novel asynchronous distributed quadratic programming method enabling independent stepsize and regularization choices for agents, improving scalability and convergence.

## Key findings

- Framework successfully solves large-scale quadratic programs
- Agents can independently choose stepsizes and regularizations
- Simulation demonstrates effective convergence and performance

## Abstract

Quadratic programs arise in robotics, communications, smart grids, and many other applications. As these problems grow in size, finding solutions becomes much more computationally demanding, and new algorithms are needed to efficiently solve them. Targeting large-scale problems, we develop a multi-agent quadratic programming framework in which each agent updates only a small number of the total decision variables in a problem. Agents communicate their updated values to each other, though we do not impose any restrictions on the timing with which they do so, nor on the delays in these transmissions. Furthermore, we allow weak parametric coupling among agents, in the sense that they are free to independently choose their stepsizes, subject to mild restrictions. We show that these stepsize restrictions depend upon a problem's condition number. We further provide the means for agents to independently regularize the problem they solve, thereby improving condition numbers and, as we will show, convergence properties, while preserving agents' independence in selecting parameters. Simulation results are provided to demonstrate the success of this framework on a practical quadratic program.