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.