|
|||||
|
|
On the solution of indefinite systems arising in nonlinear programming problems |
|
| Authors: | Silvia Bonettini Valeria Ruggiero Federica Tinti |
| Institution: | 1. Dipartimento di Matematica, Università di Ferrara, via Machiavelli 35, 44100 Ferrara, ItalyDipartimento di Matematica, Università di Ferrara, via Machiavelli 35, 44100 Ferrara, Italy===;2. Dipartimento di Matematica, Università di Ferrara, via Machiavelli 35, 44100 Ferrara, Italy |
| Abstract: | This work is concerned with the convergence properties and the numerical analysis of the preconditioned conjugate gradient (PCG) method applied to the solution of indefinite linear systems arising in nonlinear optimization. Our approach is based on the choice of quasidefinite preconditioners and of a suitable factorization routine. Some theoretical and numerical results about these preconditioners are obtained. Furthermore, we show the behaviour of the PCG method for different formulations of the indefinite system and we compare the effectiveness of the proposed variants. Copyright © 2007 John Wiley & Sons, Ltd. |
| Keywords: | preconditioned conjugate gradient method indefinite preconditioners large‐scale optimization nonlinear programming problems |