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TNPACK - A Truncated Newton Minimization Package for Large-Scale Problems:
Implementation Examples.

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We have recently presented a FORTRAN package for solving unconstrained
optimization problems by a truncated Newton algorithm. TNPACK is intended
to solve problems for which some separability and sparsity-structure information
of the Hessian is available. The Newton equations are solved approximately
at each step by a Preconditioned Conjugate Gradient method, with adaptations
to indefinite systems; the linear system involving the preconditioner is
solved by a *sparse modified* Cholesky factorization based on the
Yale Sparse Matrix Package. In this paper we describe implementation examples
on two standard optimization problems and two real-life applications. Our
intent is to aid users in their own applications, to highlight key
options and parameters that may require tailoring to the problem
and to describe application areas for which TNPACK is most suited. These
examples will illustrate various strategies for formulating preconditioners,
applying reorderings to them in order to minimize fill-in, enforcing truncation,
and dealing with indefinite regions.

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