Thursday, 13:45 - 14:10 h, Room: MA 415


Martin Weiser
Goal-oriented estimation for nonlinear optimal control problems


In optimal control problems with elliptic PDE constraints,

min J(y,u)  
s.t.  c(y,u) = 0,

the value of the cost functional is a natural quantity of interest for goal-oriented
error estimation and mesh refinement. The talk will discuss the difference between
the all-at-once error quantity J(yh,uh)-J\mathrm{opt} introduced by Becker/\allowbreak Kapp/\allowbreak Rannacher
and the black-box error quantity J(y(uh),uh)-J\mathrm{opt}. Both qualitative and
quantitative differences will be addressed for linear-quadratic problems.
In the second part, the black-box approach will be extended to smooth nonlinear problems
and will result in a novel accuracy matching for inexact Newton methods. Quantitative aspects
are illustrated on numerical examples including interior point regularizations of inequality constrained problems.


Talk 2 of the invited session Thu.2.MA 415
"Theory and methods for PDE-constrained optimization problems with inequalities" [...]
Cluster 19
"PDE-constrained optimization & multi-level/multi-grid methods" [...]


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