The approximate solution of several nonlinear optimization problems requires solving sequences of symmetric linear systems. When the number of variables is large, it is advisable to use an iterative linear solver for the Newton correction step. On the other hand, the underlying linear solver can converge slowly and the calculation of a preconditioner requires the computation of the Hessian matrix which usually represents a major task in the implementation. We propose here a way to overcome at least in part this two preconditioning issue.

Quasi matrix free preconditioners in optimization and nonlinear least-squares / S.Bellavia; D.Bertaccini; B.Morini. - STAMPA. - (2010), pp. 1036-1039. (Intervento presentato al convegno ICNAAM, Numerical Analysis and Applied Mathematics, International Conference 2010) [10.1063/1.3497801].

Quasi matrix free preconditioners in optimization and nonlinear least-squares

BELLAVIA, STEFANIA;MORINI, BENEDETTA
2010

Abstract

The approximate solution of several nonlinear optimization problems requires solving sequences of symmetric linear systems. When the number of variables is large, it is advisable to use an iterative linear solver for the Newton correction step. On the other hand, the underlying linear solver can converge slowly and the calculation of a preconditioner requires the computation of the Hessian matrix which usually represents a major task in the implementation. We propose here a way to overcome at least in part this two preconditioning issue.
2010
Numerical analysis and applied mathematics, vols I-III Book Series: AIP Conference Proceedings
ICNAAM, Numerical Analysis and Applied Mathematics, International Conference 2010
S.Bellavia; D.Bertaccini; B.Morini
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/394046
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