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

TL;DR

This paper introduces a regularized and smoothed Fischer-Burmeister method for efficiently solving convex quadratic programs in real-time, demonstrating robustness and competitiveness in model predictive control applications.

Contribution

The paper presents a novel regularized and smoothed Fischer-Burmeister approach tailored for real-time quadratic programming, enhancing practical performance and robustness.

Findings

Method is simple to implement and warmstart.

Algorithm shows robustness to early termination.

Numerical experiments demonstrate competitiveness with state-of-the-art solvers.

Abstract

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.