sci.op-research

What may not be clear to everyone is how the famous Rosenbrock
function in two variables is to be generalized or extended to higher
dimensions.
f(x) = (x_2-x_1^2)^2 + (1-x_1)^2
This function is unimodal, it has one obvious stationary point which
is a minimizer. To maintain this property terms of the same form with
x_3, x_4 etc should be added. The function becomes multimodal for
dimensions greater than 3 if instead terms with x_2, x_3, then x_3,
x_4 etc are added.
We have added both functions as Sample Submission problems to our NEOS
solver ICOS which computes all stationary points.
http://neos.mcs.anl.gov/neos/solvers/go:icos/AMPL.html

Hans Mittelmann