I believe this is equivalent to the solution given by Gene Golub in 1973 for the constraint vector required to produce a specific set of stationary values in a

I believe this is equivalent to the solution given by Gene Golub in 1973 for the constraint vector required to produce a specific set of stationary values in a linearly-constrained quadratic program where the constraint vector is unitary. https://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=9B05FFCB5C07BC4A1A2A00C7FF2C2C68?doi=10.1.1.454.9868&rep=rep1&type=pdf https://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=9B... (eq. 3.6) I haven't looked at Tao's proofs to see if this is covered, nor do I have a clear formulation of the equivalence, but it certainly is striking.