# Parallel ADMM for robust quadratic optimal resource allocation problems

## TL;DR

This paper presents a parallel GPU-based ADMM solver for quadratic resource allocation problems, demonstrating significant speedups in energy management applications for hybrid electric vehicles.

## Contribution

It introduces a novel parallel GPU implementation of ADMM tailored for quadratic problems with linear constraints, including a custom quartic minimizer.

## Key findings

- GPU implementation achieves faster computation times than serial versions.
- Application to hybrid vehicle energy management shows practical effectiveness.
- Numerical simulations validate the efficiency of the parallel approach.

## Abstract

An alternating direction method of multipliers (ADMM) solver is described for optimal resource allocation problems with separable convex quadratic costs and constraints and linear coupling constraints. We describe a parallel implementation of the solver on a graphics processing unit (GPU) using a bespoke quartic function minimizer. An application to robust optimal energy management in hybrid electric vehicles is described, and the results of numerical simulations comparing the computation times of the parallel GPU implementation with those of an equivalent serial implementation are presented.