Inexact Constraint Preconditioners for Optimization Problems

Dropping some of the elements in the Jacobian matrix A produces a significant reduction of the fill-in of the Cholesky factor of the preconditioner thus speeding-up the cost of a single iteration of the Krylov subspace method of choice. The spectral analysis of the preconditioned matrix reveals that a large number of eigenvalues are one or positive and bounded by those of . The distance of the remaining eigenvalues form unity is proven to be bounded in terms of the norm of the dropping matrix E. Some numerical results for a number of large quadratic problems demonstrate that the new approach is an attractive alternative for direct approach and for exact constraint preconditioners.