[R] optimization problem

[klausch at gmx.de]

Dear R-experts,

this is not a direct R-problem but I hope you can help me anyway.

I would like to minimize || PG-I || over P, where P is a p x p permutation matrix (obtained by permuting the rows and/or columns of the identity matrix), G is a given p x p matrix with full rank and I the identity matrix.  ||.|| is the frobenius norm.

Does anyone know an algorithm to solve such a problem? And if yes, is it implemented in R?

Currently I minimize it by going through all possible permutations - but this is not feasible for higher dimensional problems as I would like to consider too.

Any help is appreciated!

Thanks in advance,

Klaus

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