The Behavior of Newton-type Methods on Two
Equivalent Systems from Linear Programming
M.C. Villalobos, R.A. Tapia, Y. Zhang
Newton-type methods are fundamental techniques for
solving systems of nonlinear equations. However, it
is not fully appreciated that these methods can produce
significantly different behavior when applied to equivalent
systems. In this paper, we investigate differences in local
and global behavior of Newton-type methods when applied
to two different but equivalent systems from linear
programming: the optimality conditions of the logarithmic
barrier formulation and the perturbed optimality conditions.
Through theoretical analysis and numerical results, we
show Newton-type methods perform more effectively on
the latter system.
TR9802 (also report CRPC-TR98770-S)
Rice University, Computational and Applied
Mathematics, Houston, TX
September 1998
Contact: [email protected]
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