The NEOS Server offers PATH for the solution of nonlinear complementarity problems. Problems can be submitted to PATH on the NEOS server in AMPL or GAMS format.

The NEOS Server provides the current version of the PATH solver. The code is used extensively by economists for solving general equilibrium problems and is well-known to be robust and efficient on the majority of the mixed complementarity problems it encounters. The algorithm successively linearizes the normal map associated with the MCP, thereby generating a sequence of linear mixed complementarity problems. These subproblems are solved by generating a path between the current iterate and the solution of the linear subproblem; the precise details of the path generation scheme are available. A non-monotone backtracking search is performed on this path to garner sufficient decrease in its merit function, the norm of the residual of the normal map. It is known that the solutions of the subproblem will eventually provide descent for the merit function and that local superlinear or quadratic convergence will occur under appropriate conditions. A crash procedure is used to quickly identify an approximation to the active set at the solution; this is based on a projected Newton step for the normal map.

PATH was developed by
Steven Dirkse,
Michael Ferris,
and Todd Munson.

**References**

- Dirkse, S. P. and Ferris, M. C. 1997.
Crash Techniques for Large-Scale Complementarity Problems.
*Complementarity and Variational Problems: State of the Art*, SIAM Publications, Philadelphia, pp. 40-61. (crash procedure) - Dirkse, S. P. and Ferris, M. C. 1995.
The PATH Solver: A Non-Monotone Stabilization Scheme for Mixed Complementarity Problems.
*Optimization Methods and Software***5**: 123-156. (path generation scheme)

A paper describing the AMPL Complementarity Format is available. Examples of complementarity models in AMPL format can be found in the MCPLIB collection. A list of PATH options is available here.

The problem must be specified in a model file. A data file and commands
files may also be provided. If the commands file is specified, it must
contain the AMPL `solve`

command; however, it must not contain
the `model`

or `data`

commands. The model and data
files are renamed internally by NEOS.

The commands file may include option settings for the solver. To specify solver options, add

option path ampl_options 'OPTIONS';where OPTIONS is a list of one or more of the PATH options available here.

Web Submission Form

Enter the location of the AMPL model (local file)

Enter the location of the AMPL data file (local file)

Enter the location of the AMPL commands file (local file)

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