constrained linear systems

[EsmeraldaRuiz]

Hello, I was wondering if LAPACK can solve constrained linear systems
of the kind of

(L-alphaD)dY = ((dY)*D+(alpha)(dDo)...)Yo ...
with d(alpha) = y0....
and dY is perpendicular to y and dD = I and so on.
where we want to get dY for example that is the
unknown variable.

Thank you in advance !!