# A Direct Method for Parabolic PDE Constrained Optimization ProblemsCondensing

A Direct Method for Parabolic PDE Constrained Optimization Problems: Condensing [Especially on fine space discretizations we obtain large scale quadratic subproblems (5.34) in the inexact SQP method described in Chapter 5. The goal of this chapter is to present a condensing approach which is one of two steps for the solution of these large scale QPs. It consists of a structure exploiting elimination of all discretized PDE variables from the QP. The resulting equivalent QP is of much smaller, grid-independent size and can then, in a second step, be solved by, e.g., a Parametric Active Set Method (PASM) which we describe in Chapter 9.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# A Direct Method for Parabolic PDE Constrained Optimization ProblemsCondensing

Part of the Advances in Numerical Mathematics Book Series
12 pages

/lp/springer-journals/a-direct-method-for-parabolic-pde-constrained-optimization-problems-CnqxTPiUfs
Publisher
ISBN
978-3-658-04475-6
Pages
111 –122
DOI
10.1007/978-3-658-04476-3_8
Publisher site
See Chapter on Publisher Site

### Abstract

[Especially on fine space discretizations we obtain large scale quadratic subproblems (5.34) in the inexact SQP method described in Chapter 5. The goal of this chapter is to present a condensing approach which is one of two steps for the solution of these large scale QPs. It consists of a structure exploiting elimination of all discretized PDE variables from the QP. The resulting equivalent QP is of much smaller, grid-independent size and can then, in a second step, be solved by, e.g., a Parametric Active Set Method (PASM) which we describe in Chapter 9.]

Published: Nov 30, 2013

Keywords: Coarse Grid; Matrix Vector Product; Hessian Approximation; Scaling Invariance; Quadratic Subproblem