PATH

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)

Using the NEOS Server for PATH/GAMS

The user must submit a model in GAMS format to solve an optimization problem. For security purposes, the model submitted must adhere to the following conventions:

• It must be self contained, i.e., no $include or $batinclude statements.
• It may not execute external programs, i.e., no $call or execute statements.
• No file creation, i.e. no put files or $echo except for a file named 'results.txt'. Other files created in the GAMS model file will be deleted.

If you are unfamiliar with GAMS, the GAMS Documentation includes a GAMS Tutorial and User's Guide. Examples of models in GAMS format can be found in the GAMS model library.

By default, the NEOS Server limits the amount of output generated in the listing file by turning off the symbol and unique element list, symbol cross references, and restricting the rows and columns listed to zero. This behavior can be changed by specifying the appropriate options in the model file. See the documentation on GAMS output for further information.

You may optionally submit an options file if you wish to override the default parameter settings for the solver. Currently, the NEOS Server can only use optfile=1 with GAMS input. Therefore, any model that specifies a different options file will not work as intended.