Re: Minimizing the Frobenius norm

svlad wrote:
Hi,

I need to minimize the following:

E(v1....vn) = sum_{ i=1 to L } (sum_{ j=adj(i) } || Ti - Tj ||^2 )
where || . || is the Frobenius norm.

Each of the T matrices are defined in terms of the v1....vn variables.
A subset of the v1....vn variables are known in advanced.

Each matrix T is dependent on exactly four of the n variables. adj(i)
is the subset of T that are adjacent to the current Ti. Adjacency is
defined as having two of the n variables in common.

Any help would be greatly appreciated.

Having not much time, here a short hint.
You get the Frobenius norm by stacking all columns of the matrix
to get a long vector, then take the standard Euclidean norm of that
long vector, i.e. if your matrix is n x n, the vector has size sqr(n).

Now you can look at your problem as minimizing the distance of "points"
in a n^2 dimensional space.

--
Helmut Jarausch

Lehrstuhl fuer Numerische Mathematik
RWTH - Aachen University
D 52056 Aachen, Germany
.

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