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 current version of the
PATH solver
is provided by the NEOS server.
The code is extensively used 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 also available to the interested reader.
A nonmonotone 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 for 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 model is specified by a model file, and optionally,
a data file and a commands file.
If the command file is specified it must contain
the AMPL solve command.
The commands file can contain any AMPL command.
Additionally, the user can change the behaviour of the algorithm using
the standard
options for PATH.
The appropriate AMPL command is
option path ampl_options "logfile=log.tmp crash_method=none";
This sets the two options listed; any available option can be set likewise.
Printing directed to standard out 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:
Comments:
Dry run: generate job XML instead of submitting it to NEOS
Please do not click the 'Submit to NEOS' button more than once.
