Test set non linear solver

Question

what is your preferred test set to test quality of non linear solver?

this could be set of data, model and results obtained with some benchmark solver, or simply a panel of test functions that could be used to generate synthetic data.

thanks!

Answer 1

It depends a lot on which nonlinear problem you want to solve.
http://plato.asu.edu/bench.html
is a good place to start for local constrained optimization,
http://www.mat.univie.ac.at/~dferi/testenv.html
for global constrained optimization, and
http://archimedes.cheme.cmu.edu/?q=dfocomp
http://coco.gforge.inria.fr/doku.php?id=bbob-2012
for unconstrained black box optimization.

I am not aware of special test sets for nonlinear least squares.

If you know the kind of fitting problem you want to apply it to, you can generate from any known model simulated data and then compare the solutions obtained with the input for the simulation.

But if you want to have a general-purpose constrained least square solver, then you can take anyway hardly any advantage of the least squares structure. Thus it would be sensible to use (or develop) a general purpose nonlinear program solver, and test it on the test sets from one of the above sites.