### Frank E. Curtis (Lehigh University, USA)

#### An inexact active-set method for large-scale nonlinear optimization

*Friday 17 August 2012 at 15.00, JCMB Lecture Theatre C*

##### Abstract

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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