SuperADMM: Solving Quadratic Programs Faster with Dynamic Weighting ADMM

TL;DR

SuperADMM introduces a novel dynamic weighting approach to accelerate ADMM for quadratic programming, improving efficiency and accuracy over existing solvers through iterative weight updates and stability enhancements.

Contribution

The paper presents a new accelerated ADMM algorithm with dynamic constraint weighting, including stability analysis, parameter selection, and implementation for faster quadratic program solving.

Findings

SuperADMM outperforms state-of-the-art ADMM solvers in speed and accuracy.

The dynamic weighting method enhances convergence stability.

Implementation in C enables efficient execution in MATLAB and Python.

Abstract

In this paper we develop an accelerated Alternating Direction Method of Multipliers (ADMM) algorithm for solving quadratic programs called superADMM. Unlike standard ADMM QP solvers, superADMM uses a novel dynamic weighting method that penalizes each constraint individually and performs weight updates at every ADMM iteration. We provide a numerical stability analysis, methods for parameter selection and infeasibility detection. The algorithm is implemented in c with efficient linear algebra packages to provide a short execution time and allows calling superADMM from popular languages such as MATLAB and Python. A comparison of superADMM with state-of-the-art ADMM solvers and widely used commercial solvers showcases the efficiency and accuracy of the developed solver.