MINOS

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

MINOS is designed to solve "smooth" nonlinear programming (NLP) problems. Smooth nonlinear functions can be accommodated in both the objective and the constraints; nonlinear equation systems may also be solved by omitting an objective. Nonsmooth nonlinearities are also accepted, but MINOS is not designed for them and in general will not produce reliable results when they are present. MINOS also offers a primal simplex method for linear programming (LP) problems.

MINOS is suitable for large constrained problems with a linear or nonlinear objective function and a mixture of linear and nonlinear constraints. It is most efficient if the constraints are linear and there are not too many degrees of freedom.

For linear programs, MINOS uses a stable implementation of the primal simplex method. For linearly constrained problems, a reduced-gradient method is employed with quasi-Newton approximations to the reduced Hessian. For nonlinear constraints, MINOS implements a sequential linearly constrained algorithm derived from Robinson's method. Step length control is heuristic, but superlinear convergence is often achieved.

• Nonlinear objective functions and linear constraints: A reduced-gradient algorithm is used. This is an active-set method (a natural extension of the simplex method). The variables are classified as basic, superbasic, and nonbasic, with the number of superbasics indicating the effective nonlinearity of the objective. The constraints are satisfied before the objective is evaluated. Feasibility is maintained thereafter. Search directions are generated using a quasi-Newton approximation to the reduced Hessian.
• Nonlinear constraints: A projected augmented Lagrangian algorithm is used. As in Robinson's method, each major iteration solves a linearly constrained subproblem to generate a search direction. The subproblem objective is an augmented Lagrangian function. The subproblem constraints are the true linear constraints plus linearizations of the nonlinear constraints. Convergence is usually achieved, although the steplength choice is heuristic.

MINOS was developed by Bruce A. Murtagh and Michael Saunders.

Further details on MINOS can be found in the MINOS User's Manual.

Using the NEOS Server for MINOS/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.