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.

How Iteration Procedures Work