Integration of Sequential Quadratic Programming and
Domain Decomposition Methods for
Nonlinear Optimal Control Problems
M. Heinkenschloss
Department of Computational and Applied Mathematics
Rice University
D. Ridzal
Computational Mathematics and Algorithms
Sandia National Laboratories
In
Domain Decomposition Methods in Science and Engineering XVII,
U. Langer, M. Discacciati, D. Keyes, O. Widlund, and W. Zulehner (eds.),
Lecture Notes in Computational Science and Engineering Vol. 60,
Springer-Verlag, Heidelberg, 2008, pp. 69-80.
Abstract
We discuss the integration of a sequential quadratic
programming (SQP) method with an optimization-level domain decomposition
(DD) preconditioner for the solution of the quadratic optimization subproblems.
The DD method is an extension of the well-known Neumann-Neumann method
to the optimization context and is based on a decomposition of the first order
system of optimality conditions. The SQP method uses a trust-region globalization
and requires the solution of quadratic subproblems that are known to be
convex, hence solving the first order system of optimality conditions associated
with these subproblems is equivalent to solving these subproblems. In addition,
our SQP method allows the inexact solution of these subproblems and adjusts
the level of exactness with which these subproblems are solved based on the
progress of the SQP method.
The overall method is applied to a boundary control problem governed by a
semilinear elliptic equation.
Keywords
Optimal control, sequential quadratic programming,
domain decomposition, Neumann-Neumann methods
PDF file.