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 emulate the properties of Newton's method while allowing flexibility in the computational cost per iteration. Recently, we have developed a novel methodology for applying inexactness in the most fundamental iteration in constrained optimization: a line-search primal-dual Newton iteration. We have shown that our approach enjoys the same advantages as inexact Newton methods for nonlinear equations, with the only disadvantage being the difficulties associated with the presence of a barrier parameter (such as the design of preconditioners for interior-point linear systems).
In this talk we present a more general inexact Newton framework for large-scale nonlinear optimization. The main motivation for the algorithm is that we now allow the use of active-set methods for the arising large-scale quadratic subproblems (QPs). We present global convergence guarantees for our approach and discuss the critical issue of choosing the QP solver.
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