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
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.
solve
model
data
The commands file may include option settings for the solver. To specify solver options, add
option path ampl_options 'OPTIONS';