Solving Iteration Problems
Structural modeling programs generally must obtain their parameter estimates
by using iterative techniques. These techniques are special cases of nonlinear
optimization procedures for minimizing a function of n
unknowns. Nonlinear optimization is an extremely challenging area of numerical
analysis, and the problems and issues discussed in the topics on Nonlinear
Estimation remain relevant here. Any textbook on nonlinear
optimization (e.g., Dennis and Schnabel, 1983) will quickly warn the reader
that it is an art as well as a science, and that no optimization procedure
works "best" for all problems. In general, the more unknowns,
and the more nonlinear the function to be minimized, the more difficult
the problem becomes. Problems with more than 100 unknowns are, in general,
extremely difficult to solve unless you can start the iteration process
rather close to the actual solution point.
Ironically, most textbooks on structural modeling completely conceal
this fact from the reader, presenting only examples that, with respect
to the iteration process, are trivially easy and well-behaved. Armed only
with an education from such texts, the beginner to structural modeling
can be confused and frustrated by problems encountered during iteration.
If you analyze a significant number of problems with SEPATH,
you can expect to encounter iteration problems at some point. The following
topics give some guidelines for dealing with these problems.
Iteration Procedures Work
an Iteration Procedure "Hangs Up"