SuperADMM: Solving Quadratic Programs Faster with Dynamic Weighting ADMM (2506.11608v1)

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.