L. Bergamaschi, J. Gondzio, Manolo Venturin and G. Zilli,
Abstract
Issues of indefinite preconditioning of reduced Newton systems
arising in optimization with interior point methods are addressed
in this paper. Constraint preconditioners have shown much promise
in this context. However, there are situations in which an unfavorable
sparsity pattern of Jacobian matrix may adversely affect
the preconditioner and make its inverse representation unacceptably
dense hence too expensive to be used in practice. A remedy to such
situations is proposed in this paper. An approximate constraint
preconditioner is considered in which sparse approximation
of the Jacobian is used instead of the complete matrix.
Spectral analysis of the preconditioned matrix is performed
and bounds on its non-unit eigenvalues are provided.
Preliminary computational results are encouraging.
Key words: Interior-point methods, Iterative solvers, Preconditioners, Approximate Jacobian.