A Regularized and Smoothed Fischer–Burmeister Method for Quadratic Programming With Applications to Model Predictive Control

This paper considers solving convex quadratic programs 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 a 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.