Invited Session Tue.2.H 0110

Tuesday, 13:15 - 14:45 h, Room: H 0110

Cluster 16: Nonlinear programming [...]

Nonlinear optimization V


Chair: Frank E. Curtis and Daniel Robinson



Tuesday, 13:15 - 13:40 h, Room: H 0110, Talk 1

Denis Ridzal
A matrix-free trust-region SQP algorithm for large-scale optimization

Coauthors: Miguel Aguilo, Joseph Young


We present an inexact trust-region sequential quadratic
programming (SQP) method for the matrix-free solution of
large-scale nonlinear programming problems. First, we
discuss recent algorithmic advances in the handling of
inequality constraints. Second, for optimization problems
governed by partial differential equations (PDEs) we
introduce a class of preconditioners for optimality
systems that are easily integrated into our matrix-free
trust-region framework and that efficiently reuse the
available PDE solvers. We conclude the presentation with
numerical examples in acoustic design, material inversion
in elastodynamics and optimization-based failure analysis.



Tuesday, 13:45 - 14:10 h, Room: H 0110, Talk 2

Anders Forsgren
Inexact Newton methods with applications to interior methods


Newton's method is a classical method for solving a nonlinear equation. We discuss how Jacobian information may be reused without sacrificing the asymptotic rate of convergence of Newton's method. In particular, we discuss how inexact Netwon methods might be used in the context of interior methods for linear and convex quadratic programming.



Tuesday, 14:15 - 14:40 h, Room: H 0110, Talk 3

Wenwen Zhou
Numerical experience of a primal-dual active set method and its improvement

Coauthor: Joshua Griffin


SAS has recently developed and implemented a multi-threaded Krylov-based active set method based on the exact primal dual augmented Lagrangian merit function of P. E. Gill and D. Robinson [1] for large-scale nonconvex optimization. The merit function has several attractive properties, including a dual regularization term that effectively relaxes restrictions for what preconditioner types can be used with the corresponding Newton equations. Numerical experience and strategies for improving convergence for this approach will be reported in this talk.

  1. P. E. Gill and D. P. Robinson, A Primal Dual Augmented Lagrangian, Department of Mathematics, University of California San Diego. Numerical Analysis Report 08-2.


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