[BANANA] LA/Opt seminar TODAY (Martin Stoll)

[Michael A. Saunders]

Reminder: Extra matrix computation seminar today.
           Preconditioning for PDE-constrained optimization
           NOTE DIFFERENT ROOM: TERMAN 453

           Next week: No seminar because of SIAM meeting in Monterey.
           Wed Nov 4: Chris Paige


    Linear Algebra and Optimization Seminar (CME 510)
    iCME, Stanford University
    http://icme.stanford.edu/seminars/seminars.php

    4:15pm Fri Oct 23, 2009
    Terman 453

    Martin Stoll
    Oxford University Computing Laboratory, UK
    martin.stoll80 at googlemail.com
    http://people.maths.ox.ac.uk/~stoll/

Preconditioning for PDE-constrained optimization

Advances in algorithms and hardware have enabled more research on the
optimization of functions with constraints given by partial
differential equations.  Problems of this type arise in a variety of
applications and pose significant challenges to optimization
algorithms and numerical methods.  In this talk we present
preconditioners for problems in a general setup and also when
additional box constraints are introduced for the control.  These
constraints add an extra layer of complexity to the optimization
method and the efficient solution of the linear system is very
important.

Block-diagonal preconditioners present one possibility to solve the
arising saddle point problems efficiently.  In addition, we discuss
the use of block-triangular preconditioners that can be used in a
non-standard inner product iterative method.  We show that the
drawbacks of this method can be easily overcome by choosing
appropriate preconditioners for the blocks of the saddle point system.
We present an eigenvalue analysis for the preconditioners and
illustrate their competitiveness on some examples.

If time permits we will discuss some recent developments of using
these preconditioners for the solution of Allen-Cahn variational
inequalites.  This is joint work with Andy Wathen and Tyrone Rees.