An Analysis of Newton's Method for Equivalent Karush--Kuhn--Tucker
In this paper we analyze the application of Newton's method to the solution
of systems of nonlinear equations arising from equivalent forms of the first--order
Karush--Kuhn--Tucker necessary conditions for constrained optimization.
The analysis is carried out by using an abstract model for the original system of
nonlinear equations and for an equivalent form of this system obtained
by a reformulation that
appears often when dealing with first--order Karush--Kuhn--Tucker necessary conditions.
The model is used to determine the quantities that bound the difference between
the Newton steps corresponding to the two equivalent systems of equations.
The model is sufficiently abstract to include the cases of equality--constrained
optimization, minimization with simple bounds, and also a class of discretized optimal