A bounded-variable least-squares solver based on stable QR updates

In this paper, a numerically robust solver for least-squares problems with bounded variables (BVLS) is presented for applications including, but not limited to, model predictive control (MPC). The proposed BVLS algorithm solves the problem efficiently by employing a recursive QR factorization method based on Gram-Schmidt orthogonalization. A reorthogonalization procedure that iteratively refines the QR factors provides numerical robustness for the described primal active-set method, which solves a system of linear equations in each of its iteration via recursive updates. The performance of the proposed BVLS solver, that is implemented in C without external software libraries, is compared in terms of computational efficiency against state-of-the-art quadratic programming solvers for small to medium-sized random BVLS problems and a typical example of embedded linear MPC application. The numerical tests demonstrate that the solver performs very well even when solving ill-conditioned problems in single precision floating-point arithmetic.