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

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.