# FBstab: A Stabilized Semismooth Quadratic Programming Algorithm with Applications in Model Predictive Control

## TL;DR

FBstab is a new robust algorithm for convex quadratic programming that combines proximal point and semismooth Newton methods, showing strong performance in model predictive control applications.

## Contribution

The paper introduces FBstab, a novel algorithm that improves robustness, warmstarting, and handling of degenerate solutions in quadratic programming.

## Key findings

- FBstab is numerically robust and easy to warmstart.
- It handles degenerate primal-dual solutions and detects infeasibility.
- FBstab often outperforms existing methods in benchmarks.

## Abstract

This paper introduces the proximally stabilized Fischer-Burmeister method (FBstab); a new algorithm for convex quadratic programming that synergistically combines the proximal point algorithm with a primal-dual semismooth Newton-type method. FBstab is numerically robust, easy to warmstart, handles degenerate primal-dual solutions, detects infeasibility/unboundedness and requires only that the Hessian matrix be positive semidefinite. We outline the algorithm, provide convergence and convergence rate proofs, report some numerical results from model predictive control benchmarks, and also include experimental results. We show that FBstab is competitive with and often superior to, state of the art methods, has attractive scaling properties, and is especially promising for model predictive control applications.