# Improving the Optimization Techniques in LaueView

### S.J. Wright, Z. Ren*, R. Sheng, M. Nayakkankuppam

MCS Division, Argonne National Laboratory, *University of Chicago

The LaueView code described by Ren and Moffatt make use of a variety
of numerical analysis and optimization techniques. Essentially, the
problem is one of fitting a model to observed data using a
least-squares measure of the goodness of fit. Major issues that arise
include (i) parametrizing the model and (ii) efficient choice and
implementation of an algorithm for the nonlinear least-squares
problem.

In this talk with describe our experience to date with the second
topic. We describe a trust-region Levenberg-Marquardt algorithm that
has proved to be more efficient than the previously implemented
strategy, yielding speedups of
between 3 and 10 on most of the data sets we tested.
We will discuss how the textbook Levenberg-Marquardt implementation
had to be adapted to the requirements of the problem at hand (in
particular, the fact that a Jacobian matrix cannot be computed
explicitly because it is simply too large.) Much of the savings came
from a decoupling of the fitting function evaluation from the more
expensive derivative evaluation, so that new derivatives were
evaluated only after a successful step had been taken. We also discuss
"details" that were significant in improving the efficiency and
robustness, such as speedup of a time-critical loop involving
intrinsic FORTRAN functions and the use of double precision
accumulation in evaluation of the approximate Hessian. Finally, we
discuss plans for testing alternative, more compact parametrizations
of the model, which may improve both the efficiency, robustness, and
accuracy of LaueView.

Our experiences in detecting and speeding up time-critical sections of
the code by using techniques from numerical analysis, and in
encapsulating the complex parts of the code to make possible the use
of more powerful optimization techniques, will certainly be relevant
to other codes to be discussed at the meeting
.

(posted 21-Oct-97 jw)