Mathematics and Computer Science Division
Argonne National Laboratory
Preconditioning Newton's Method
Abstract
We describe current research on the development
of the ELSO environment for the solution of
large-scale optimization problems.
An important goal of this research is the ability to solve
large-scale problems while only requiring that the user
provide code for the evaluation of a partially separable function.
The development of ELSO is important because it
eliminates the need to provide the gradient and sparsity pattern;
in all other approaches the user needs to provide this information.
In the current environment a trust region Newton method
is used to solve the optimization problem and ADIFOR/SparsLinc
is used to compute derivatives.
In this talk we describe the theory and implementation of
the trust region Newton method in ELSO.
We emphasize the central role played by the choice
of an incomplete Cholesky
factorization as a preconditioner (scaling matrix) for
the trust region method.