PATHNLP

The NEOS Server offers PATHNLP for the solution of nonlinearly constrained optimization problems. Problems can be submitted to PATHNLP on the NEOS server in GAMS format.

PATHNLP is a solver for nonlinear programming (NLP) problems. PATHNLP finds stationary points for nonlinear programs by internally constructing the Karush-Kuhn-Tucker (KKT) system of first-order optimality conditions and solving this system using the PATH Solver for complementarity problems. The solution to the original NLP is extracted from the KKT solution and returned to GAMS. All of this takes place automatically - no special syntax or user reformulation is required.

Typically, PATHNLP works very well for convex models. It also has a comparative advantage on models whose solution via reduced gradient methods results in a large number of superbasic variables, since the PATH solver won't construct a dense reduced Hessian in the space of the superbasic variables as reduced gradient solvers do. For nonconvex models, however, PATHNLP is not as robust as the reduced gradient methods.

Algorithmic details also can be found in reports by the original developers of PATH: Steven Dirkse, Michael Ferris, and Todd Munson. Documentation for PATHNLP is available on the GAMS/PATHNLP webpage.

Using the NEOS Server for PATHNLP/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.