GAMS/PATH User Guide Version 4.3

of preprocessing and can be used to solve constrained systems of nonlinear
equations. The output for PATHC is identical to the main distribution described
in Section 2.1 with additional output for preprocessing. The options
are the same between the two versions.
2.5.1 Preprocessing
The preprocessor is work in progress. The exact output in the final
version may differ from that given below.
The purpose of a preprocessor is to reduce the size and complexity of
a model to achieve improved performance by the main algorithm. Another
benefit of the analysis performed is the detection of some provably unsolvable
problems. A comprehensive preprocessor has been incorporated into PATHC
as developed in [18].
The preprocessor reports its finding with some additional output to the
log file. This output occurs before the initial point statistics. An example of
the preprocessing on the forcebsm model is presented below.
Zero: 0 Single: 112 Double: 0 Forced: 0
Preprocessed size: 72
The preprocessor looks for special polyhedral structure and eliminates variables
using this structure. These are indicated with the above line of text.
Other special structure is also detected and reported.
On exit from the algorithm, we must generate a solution for the original
problem. This is done during the postsolve. Following the postsolve, the
residual using the original model is reported.
Postsolved residual: 1.0518e-10
This number should be approximately the same as the final residual reported
on the presolved model.
2.5.2 Constrained Nonlinear Systems
Modelers typically add bounds to their variables when attempting to solve
nonlinear problems in order to restrict the domain of interest. For example,
many square nonlinear systems are formulated as
F (z) =0,ℓ≤ z ≤ u,
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