Eigenvalues as objective function?

[matthias....@gmail.com]

Dear Google-Group,

I want to build an objective function in AMPL based on the Eigenvalues of a matrix within my *.mod file for solving a DoE problem. Has anyone experience in calculating Eigenvalues in AMPL for e.g. 10x10 - 100x100 matrices? The matrix is often singular and I expect some Eigenvalues to be 0. I tried to solve the characteristic polynomial det(A-lambda*E) = 0 s.t. det(A) = prod(lambda) and trace(A) = sum(lambda). The determinant was calculated with LU decomposition (Crout algorithm). This approach worked fine for some 3x3 test matrices but fails with my "real" problem. Is there a more robust approach? I would be very glad about some pseudo-code.

Thanks in advance!

[e.d.an...@mosek.com]

My guess is that what you have tried leads to something highly nonconvex which may not be that robust. Sometimes you can formulate stuff with eigenvalues as a semidefinite optimization model that is convex hence is more robust to solve.

Here is a couple of links

   http://en.wikipedia.org/wiki/Semidefinite_programming

   http://docs.mosek.com/generic/modeling-letter.pdf

[Robert Fourer]

Is "A" a matrix of parameters or a matrix of variables?

Bob Fourer
4...@ampl.com

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