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
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
PATH was developed by
and Todd Munson.
A paper describing the AMPL
Complementarity Format is available.
Examples of complementarity models in AMPL format can be found in the
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';