Iterative solvers appear to be very promising in the development of efficient software, based on Interior Point methods, for large-scale nonlinear optimization problems. In this paper we focus on the use of preconditioned iterative techniques to solve the KKT system arising at each iteration of a Potential Reduction method for convex Quadratic Programming. We consider the augmented system approach and analyze the behaviour of the Constraint Preconditioner with the Conjugate Gradient algorithm. Comparisons with a direct solution of the augmented system and with MOSEK show the effectiveness of the iterative approach on large-scale sparse problems. © 2007 Springer Science+Business Media, LLC.
On the iterative solution of KKT systems in potential reduction software for large-scale quadratic problems / Cafieri, S.; D'Apuzzo, M.; De Simone, V.; Di Serafino, D.. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - 38:1(2007), pp. 27-45. [10.1007/s10589-007-9035-y]
On the iterative solution of KKT systems in potential reduction software for large-scale quadratic problems
Di Serafino D.
2007
Abstract
Iterative solvers appear to be very promising in the development of efficient software, based on Interior Point methods, for large-scale nonlinear optimization problems. In this paper we focus on the use of preconditioned iterative techniques to solve the KKT system arising at each iteration of a Potential Reduction method for convex Quadratic Programming. We consider the augmented system approach and analyze the behaviour of the Constraint Preconditioner with the Conjugate Gradient algorithm. Comparisons with a direct solution of the augmented system and with MOSEK show the effectiveness of the iterative approach on large-scale sparse problems. © 2007 Springer Science+Business Media, LLC.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
