ITLApplied  Computational Mathematics Division
ACMD Seminar Series
Attractive Image NIST

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)
Thursday, May 1, 2003 13:00-14:00,
Room 4550

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. Kearsley

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