Large-Scale Optimization Techniques for the Regularization of Ill-Posed
Problems
Marielba Rojas
Department of Mathematics, Wake Forest University
Thursday, May 1, 2003 15:00-16:00,
Room 145, NIST North (820)
Gaithersburg
Thursday, May 1, 2003 13:00-14:00,
Room 4550
Boulder
Abstract:
We will discuss the use of optimization techniques, in particular,
trust-region techniques,
in the solution of large-scale inverse problems. We will describe the
matrix-free method
LSTRS for the large-scale trust-region subproblem (TRS) of minimizing a
quadratic functional
subject to a norm constraint. The method is based on a reformulation of
the TRS as a parameterized
eigenvalue problem. The strategy consists of an iterative procedure that
drives the parameter
toward its optimal value. The solution to the TRS is then recovered from
the solution of the
eigenvalue problem corresponding to the optimal parameter. A large-scale
eigenvalue
problem must be solved at each iteration. This is accomplished by means
of the Implicitly
Restarted Lanczos Method.
We will describe the method, discuss the issues associated with
ill-posed problems, and
present numerical results on large-scale inverse problems. The results
were obtained with
a MATLAB implementation of LSTRS. A MATLAB 6 version of LSTRS will be
publicly
available shortly. The problems discussed include large-scale seismic
inversion problems
with field data.
Contact: A. J. KearsleyNote: Visitors from outside NIST must contact
Robin Bickel; (301) 975-3668;
at least 24 hours in advance.
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