For an approach to the Hadamard-matrix-problem: is there a proof, that the iterative plane-wise orthogonal rotations (Quartimax/Varimax) converge to global maximum?

While waiting for Will Orrick to weigh in, I have an unprofessional opinion which says that this approach is unlikely to be more productive than many combinatorial approaches for finding D-optimal binary matrices.

There may be some interesting techniques used that will avoid local minima, but the problem smells to me like finding optimal minima of a function for which it can be proven that such minima are found at integral values of the arguments, but that only 1 out of every 2^(n log n) such is an actual optimal minimum. Your function has provably many global minima, and very likely exponentially more local minima. Unless you have a technique for smelling deep gopher holes ins field, you are going to end up checking a lot of shallow gopher holes. And this is for dimensions as small as n=8, where we know ahead of time what all the global minima will look like and where they will be found. If the algorithm does no better than, say, 50% success for this dimension, I expect its chances of success to be superexponentially decreasing as the dimension grows by 4.

On the plus side, I don't know about this algorithm, so there may indeed be a different smell to a deep gopher hole that this algorithm has.

Gerhard "We Need Bill Murray Now" Paseman, 2012.03.08