The NEOS Server offers MILES for the solution of mixed complementarity problems in GAMS format.

MILES is a Fortran program for solving nonlinear complementarity problems and nonlinear systems of equations. The solution procedure is a generalized Newton method with a backtracking line search. This code is based on an algorithm investigated by Mathiesen (1985) who proposed a modeling format and sequential method for solving economic equilibrium models. In this implementation, subproblems are solved as linear complementarity problems (LCPs), using an extension of Lemke's almost-complementary pivoting scheme in which upper and lower bounds are represented implicitly. The linear solver employs the basis factorization package LUSOL, developed by Gill et al. (1991)

MILES was originally developed by
Thomas F.
Rutherford.
The documentation for MILES is available on the
GAMS Solvers
website.

**References:**

- Gill, P. E., Murray, W., Saunders, M. A., and Wright, M.H. 1991. Maintaining LU factors of a general sparse matrix. Linear Algebra and its Applications 88/89: 239-270.
- Mathiesen, L. 1985. Computation of economic equilibria by a sequence of linear complementarity problems. Mathematical Programming Study 23.

The user must submit a model in GAMS format to solve an optimization problem. For security purposes, the model submitted must adhere to the following conventions:

- It must be self contained, i.e., no $include or $batinclude statements.
- It may not execute external programs, i.e., no $call or execute statements.
- No file creation, i.e. no put files or $echo except for a file named 'results.txt'. Other files created in the GAMS model file will be deleted.

If you are unfamiliar with GAMS, the GAMS Documentation includes a GAMS Tutorial and User's Guide. Examples of models in GAMS format can be found in the GAMS model library.

By default, the NEOS Server limits the amount of output generated in the listing file by turning off the symbol and unique element list, symbol cross references, and restricting the rows and columns listed to zero. This behavior can be changed by specifying the appropriate options in the model file. See the documentation on GAMS output for further information.

You may optionally submit an options file if you wish to override the default parameter settings for the solver.
Currently, the NEOS Server can only use **optfile=1** with GAMS input. Therefore, any model that specifies a different options file will not work as intended.

Web Submission Form

You can submit an optimization problem specified in the GAMS modeling
language to be solved using the optimization tools on the NEOS Server.
You need to specify the absolute path to a GAMS file on your
system.

The Options file is optional and requires that the
statement
exist before the solve statement in your model file. At this
time, only is supported; however,
options may also be specified within the model input file (see
the GAMS documentation).

`<modelname>.optfile = 1 ;`

`optfile = 1`

Optional GDX file for inputs. This file will be renamed to in.gdx. The
model must include "$GDXIN in.gdx" to load this file.

The solver will return a compressed GDX file which contains all
symbols in the model.

The log file contains information generated by the algorithm
during a solve. Checking the box will cause the log file to be
included in the output returned.

Enter any additional comments here (e.g. to identify the data
for your own information). These comments will be returned
with your results.

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