FBstab: A proximally stabilized semismooth algorithm for convex quadratic programming

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