On the Solution of Indefinite Systems Arising in Nonlinear Optimization
Abstract
This work is concerned with the solution of a class of symmetric
indefinite linear systems of equations, typically arising in
nonlinear optimization: indeed, the solution of such system is
crucial for determining the search direction of many
Interior--Point methods. Our approach is based on the preconditioned
conjugate gradient method with the
choice of a quasidefinite preconditioner and of a suitable
Cholesky--like factorization subroutine. We show a numerical comparison of the
performances of the preconditioned conjugate gradient method
applied to different formulations of the linear system.
[DOI: 10.1685 / CSC06025] About DOI
indefinite linear systems of equations, typically arising in
nonlinear optimization: indeed, the solution of such system is
crucial for determining the search direction of many
Interior--Point methods. Our approach is based on the preconditioned
conjugate gradient method with the
choice of a quasidefinite preconditioner and of a suitable
Cholesky--like factorization subroutine. We show a numerical comparison of the
performances of the preconditioned conjugate gradient method
applied to different formulations of the linear system.
[DOI: 10.1685 / CSC06025] About DOI
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PDFDOI: https://doi.org/10.1685/
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