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The Role of linear Objective Functions in Barrier Methods

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Florian Jarre and Stephen Wright

We consider the asymptotic behavior of the Newton/log barrier method
for inequality constrained optimization. We show that, when the
objective function is linear, an effective step can be taken along the
Newton direction after each reduction in the barrier parameter,
leading to efficient performance during the final stages of the
algorithm. This behavior contrasts with the case of a nonlinear
objective, where Newton's method often performs more and more poorly
as the barrier parameter is reduced to zero. We analyze the behavior
and demonstrate our result on a simple example.
wright@mcs.anl.gov

Preprint MCS-P485-1294, MCS Division, Argonne National Laboratory.
(Revised, August, 1997.)