A chordal preconditioner for large-scale optimization

@article{Coleman1988ACP,
  title={A chordal preconditioner for large-scale optimization},
  author={Thomas F. Coleman},
  journal={Mathematical Programming},
  year={1988},
  volume={40},
  pages={265-287}
}
We propose an automatic preconditioning scheme for large sparse numerical optimization. The strategy is based on an examination of the sparsity pattern of the Hessian matrix: using a graph-theoretic heuristic, a block-diagonal approximation to the Hessian matrix is induced. The blocks are submatrices of the Hessian matrix; furthermore, each block is chordal. That is, under a positive definiteness assumption, the Cholesky factorization can be applied to each block without creating any new… CONTINUE READING