GAMS

GAMS is a programming language and software suite to model mathematical optimization problems. It enables a wide variety of models to be described with many thousands of variables. Running a GAMS problem solves the models described in the source code, but can also do other things. The language is proprietary. A number of file types and extensions are used by GAMS:

.gms
The main source code for a GAMS project is in one or more text files ending with .gms extensions. This defines variables, equations, and other important parts of the model definition.

.opt
These are options files for specific solvers in GAMS. They may have secondary extensions after the  to distinguish them, as their file name determines which solver they affect. For example, a CPLEX options file may be named, or   to distinguish it from other options files for that solver. According to GAMS, these may also end in  or.

.gdx
GDX files are binary data files. These can be read and edited with GAMS, or with other programming languages using libraries that are included as part of GAMS.

.inc
"Include files." I have no idea what these are, but they're apparently text files.

.lst, .lxi, .ref
These are text files created by GAMS. files show logs and results from the solving process. files are a sort of intermediate language. files are used for debugging. LST files are also called "MASM Listing" files, however, they should not be confused with Microsoft Assembler files (also called MASM).

.efi
Short for "External files", these are text files which denote which files need to be sent when using cloud computing.

Other files
GAMS also may use a YAML file called, and supposedly also   "reference" files, but I don't know anything about that one.

References and more information

 * GAMS on Wikipedia
 * GAMS language documentation
 * GDX files
 * Short info and examples for .lst and .lxi files
 * .ref files in the GAMS viewer
 * Some info on .efi files