Title: Inexact Newton Method for Nonlinear Constrained Optimization

Inexact Newton methods play a fundamental role in the solution of large-scale
unconstrained optimization problems and nonlinear equations.  The key advantage
of these approaches is that they can be made to emulate the properties of
Newton's method while allowing flexibility in the computational cost per
iteration.  Due to the multi-objective nature of *constrained* optimization
problems, however, that require an algorithm to find both a feasible and
optimal point, it has not been known how to successfully apply an inexact
Newton method within a globally convergent framework.

In this talk, we present a new methodology for applying inexactness to the most
fundamental iteration in constrained optimization: a line-search primal-dual
Newton algorithm.  We illustrate that the choice of merit function is crucial
for ensuring global convergence, and discuss novel techniques for handling
non-convexity, ill-conditioning, and the presence of inequality constraints in
such an environment.  Preliminary numerical results are presented for
PDE-constrained optimization problems.