🚀 go-pugleaf

Hi,

 I had a (probably naive) question about an optimization problem that
I am trying to solve:

              min  F(x)      subject to
               x

                g_i[\lambda_i(x)] < 0,  i = 1,...,n

where \lambda_i is the i-th eigenvalue of some matrix. \lambda is a function
of x and the constraint g_i is a function of \lambda_i. The function F and
the constraints g are non-linear. When I compute the eigenvalues \lambda_i,
I sort the eigenvalues by the absolute value thus deciding the "ordering" of
the constraints. It is possible (I think so) that during the optimization
process, the "ordering" changes e.g. the 1st eigenvalue could become the
2nd and vice versa.

Now the questions:

1) does such a change in the ordering of the constraints
during the optimization, affect the process? adversely?

(I have tried this out on MATLAB using CONSTR.M and it seems to work most
of the times. The few times it did'nt work, it would say that it was
infeasible. Hence I was wondering about the effect of "ordering")

2) is there a neat way to "track" the eigenvalues such that the
"ordering" remains intact?

Thanks in advance for answers/pointers.

-sriram.

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Sriram Srinivasan                       ss4i@kelvin.seas.virginia.edu
Dept. of Mech. & Aero. Engg.
Univ. of Virginia.
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