Geometrically, scaling and preconditioning seem to address similar challenges in optimization. However, these two concepts are implemented very differently. Take trust region Newton method, as an example. When a problem is poorly scaled, an elliptical trust region is recommended. Is it possible to formulate an equivalent preconditioner based approach such that one works with spherical trust regions?update: Section 7.5 in Practical Optimization by Gill , Murray & Wright gives a clear connection between variable scaling and preconditioning the hessian.
scaling and preconditioning for trust region Newton methods
optimization;numerical analysis;newton method;trust regions
The ideas are certainly related, at the very least if your preconditioner corresponds to a symmetric and positive definite matrix. This is because in that case, preconditioning simply means using a different inner product, i.e., a different metric. This can be interpreted  as saying that what is a very elongated ellipsoid in the usual $l_2$ metric may turn out to be much closer to a sphere in the preconditioner metric. This picture is valid because the application of an SPD preconditioner can be interpreted as a rotation, axis-parallel scaling, and inverse rotation.The picture becomes much less clear to interpretation if you use preconditioners that correspond to indefinite or non-symmetric matrices since these can then no longer be interpreted as a simple change in metric.