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The NEOS Server offers PATH for the solution of nonlinear complementarity problems in AMPL format. A paper describing the AMPL Complementarity Format is available.

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.

Using the NEOS Server with PATH

The user must submit a model in AMPL format to solve a nonlinear complementarity problem. Examples of complementarity models in AMPL format can be found in the MCPLIB collection.

The complementarity problem must be specified by a model file with the options of a data file and a commands file. If the commands file is specified, it must contain the AMPL solve; command. However, the commands file must not contain the model or data commands. The model and data files are renamed internally by NEOS.

The commands file may include AMPL commands and option settings for PATH. 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. Printing directed to standard output is returned to the user with the output.

Enter the location of the AMPL model (local file)
Model File:

Enter the location of the AMPL data file (local file)
Data File:

Enter the location of the AMPL commands file (local file)
Commands File:


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