NOP

NOP is a compact input format for nonlinear optimization problems.

The NOP format is a nonlinear analogue of an explicit representation of sparse matrices by means of index lists and values of the corresponding matrix entries. Thus the format abstracts from the meaning of the problem and hence does not allow names for variables or parameters, but it explicitly displays the internal (e.g., least squares or partially separable) structure of the problem. This is a very useful feature for global or large scale local optimization.

The amount of overhead in the formulation of smaller problems is very slight: For example, Rosenbrock's function with bound constraints,

can be represented in a few lines:
Explicitly, we introduce additional variables
x_3=10x_1^2-10x_2=0x_1-10x_2+10x_1^2+0x_2
coded in the qu4 element, and
x_4=(x_3-0)^2+(x_1-1)^2x_3^2+(x_1-1)^2
coded in the qu2 element.

Together with an interface to GLOPT, a global constrained optimization code under development in Vienna (not yet ready for release...), and with a planned interface to the modeling language AMPL (by R. Fourer, D.M. Gay and B.W. Kernighan) to allow the automatic structuring of input on a higher level, this is a promising tool for the formulation and solution of nonlinear optimization problems. For details, see the paper
NOP - a compact input format for nonlinear optimization problems.

Currently, we have coded over 50 popular test problems, and the list can be expected to grow. You may access the NOP files from the NOP Library of Global Optimization Test Problems

When our NOP development is finalized, we plan to make publicly available (perhaps at the end of 1996) a NOP reader that produces Fortran 77 subroutines for function evaluation, enclosures, underestimators, etc. for a given NOP file so that people can use them in their own algorithms.

The Vienna research group is developing a branch and bound code that solves constrained global optimization problems given in the NOP format. At the current stage of development we can solve to optimality about half of the coded problems. However, these are just the beginnings... For details, see the paper
GLOPT - A Program for Constrained Global Optimization.

You are invited to contribute to the NOP library by sending new items (and maybe we'll solve it for you)! You are also invited to submit suggestions and criticism on the present version (which is NOP1.0);


Global Optimization
my home page (http://www.mat.univie.ac.at/~neum)

Arnold Neumaier (Arnold.Neumaier@univie.ac.at)