# A Regularized and Smoothed Fischer-Burmeister Method for Quadratic Programming with Applications to Model Predictive Control

arXiv: https://arxiv.org/abs/1807.03214 · HTML: https://mlsanity.com/paper/1807.03214/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2018.

## Built on by (most cited first, 4 of 4)

- [Model Predictive Control and Reinforcement Learning: A Unified Framework Based on Dynamic Programming](https://mlsanity.com/paper/2406.00592/) (2024)
- [An Intelligent Self-driving Truck System For Highway Transportation](https://mlsanity.com/paper/2112.15304/) (2021)
- [Elastic ODYN: Differentiable Optimization for Infeasible Control and Learning in Robotics](https://mlsanity.com/paper/2606.16564/) (2026)
- [A Scalable Learned Iterative Solver for Nonlinear MPC via Temporal Decomposition](https://mlsanity.com/paper/2610.13480/) (2026)

## Abstract (arXiv)

This paper considers solving convex quadratic programs (QPs) in a real-time setting using a regularized and smoothed Fischer-Burmeister method (FBRS). The Fischer-Burmeister function is used to map the optimality conditions of the quadratic program to a nonlinear system of equations which is solved using Newton's method. Regularization and smoothing are applied to improve the practical performance of the algorithm and a merit function is used to globalize convergence. FBRS is simple to code, easy to warmstart, robust to early termination, and has attractive theoretical properties, making it appealing for real-time and embedded applications. Numerical experiments using several predictive control examples show that the proposed method is competitive with other state of the art solvers.