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.

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

Nilay Saraf;Alberto Bemporad
2020

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11771/14327
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