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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