This paper proposes a new algorithm for solving convex quadratic programs (QP) subject to linear inequality and equality constraints. The method extends an approach recently proposed by the author for solving strictly convex QP's using nonnegative least squares, by making it numerically more robust and able to handle also the nonstrictly convex case, equality constraints, and warm starting from an initial guess. Robustness is achieved by introducing an outer proximal-point iteration scheme that regularizes the problem without altering the solution, and by adaptively weighting the least squares problems encountered while solving the problem. The performance of the resulting QP solver in terms of speed and robustness in the single precision arithmetic is assessed against other optimization algorithms tailored to embedded model predictive control applications.

A numerically stable solver for positive semi-definite quadratic programs based on nonnegative least squares

Bemporad A
2018-01-01

Abstract

This paper proposes a new algorithm for solving convex quadratic programs (QP) subject to linear inequality and equality constraints. The method extends an approach recently proposed by the author for solving strictly convex QP's using nonnegative least squares, by making it numerically more robust and able to handle also the nonstrictly convex case, equality constraints, and warm starting from an initial guess. Robustness is achieved by introducing an outer proximal-point iteration scheme that regularizes the problem without altering the solution, and by adaptively weighting the least squares problems encountered while solving the problem. The performance of the resulting QP solver in terms of speed and robustness in the single precision arithmetic is assessed against other optimization algorithms tailored to embedded model predictive control applications.
2018
Active-set methods; model predictive control (MPC); nonnegative least squares; proximal-point method; quadratic programming;
File in questo prodotto:
File Dimensione Formato  
08000691.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Nessuna licenza
Dimensione 501.36 kB
Formato Adobe PDF
501.36 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11771/3663
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 21
social impact