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For the numerical solution of all problems considered in the following section
a combination of the AMPL [12] algebraic *modeling language* and the
*interior point* solver LOQO [23] proved to be both convenient
and powerful. In order to make the formulation of mathematical optimization
problems generic and independent of both the actual solver used and the
programming language it is written in, modeling languages were developed.
AMPL provides interfaces to a large number of solvers, both commercial
and free-for-research codes. One of the latter ones is LOQO which grew
out of an interior point LP optimizer to a convex QP and very recently to a
general NLP solver implementing an interior point approach. Although the
code is currently still being perfected it proved to be very efficient
for the solution of *large-scale* nonlinear problems in the benchmarks
of [21]. It was thus chosen for the following computations;
see also the comparison in Example 5.1 below.
It should be remarked that LOQO implements an infeasible primal-dual
path-following method. The KKT necessary conditions are essentially solved
as a system of nonlinear equations with a Newton-like method. Therefore,
it causes no problem if iterates are not feasible because it only means
that residuals or right-hand sides corresponding to the equality constraints
are not zero. At least asymptotically feasibility will be attained.
Another feature that makes AMPL attractive and that was exploited is
its *automatic differentiation* capability. Only functions for objective
and constraints need to be provided.

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*Hans D. Mittelmann *

2002-11-25