Model Problems for Large-Scale Optimization

Brett M. Averick and Jorge J. Moré

As part of the MINPACK-2 project, we have developed a collection of large-scale optimization problems. The problems in this collection are representative of interesting optimization problems that arise in applications, for example, fluid dynamics, medicine, elasticity, combustion, molecular design, nondestructive testing, chemical kinetics, lubrication, optimal design, and superconductivity. Software is provided to evaluate the function and Jacobian matrices for systems of nonlinear equations and nonlinear least squares, and functions and gradients for minimization problems. We have also developed software to define the sparsity pattern of all the large-scale problems, as well as Jacobian-vector products for systems of nonlinear equations and Hessian-vector products for minimization problems.

The README file contains a description of the problems. For additional information on the problems, see the user guide .

The tar file minpack2-probs contains source for the model problems.

All of the problems in this collection have interesting features. Below is a plot of a complex-valued function (the order-parameter) associated with a problem in this collection: The 2-dimensional Ginzburg-Landau problem. This is a large-scale non-convex optimization problem whose solution requires high-accuracy.

 


Argonne National Laboratory / more@mcs.anl.gov