? analytic constraint optimization

Hi:

Usually when searching for the optimal soln of a constrained optimization,

we use iterative method to do that and need to be aware of whether the
obtained

soln is global or only local. It'd be good if we can transform the problem
to

other form that has better analytical property.

For example, A and B are both semi-positive definite Hermitian matrices.

We want to find the maximal of f(u) = u*A*u subjected to the constraint

g(u) = u*B*u <= c (the constraint), u is complex.

I heard that this can be transformed to an eigenvalue problem but don't
see

how. Anyone knows how to do this?

Thanks,
by Cheng Cosine
May/19/2k7 NC


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