Just a question about a literature reference. I am writing a paper for engineers.
Usually for the Lagrange multiplier problem
$$ \nabla f(x)+\lambda \nabla g(x)=0 $$
the sensitivity result that the multiplier $\lambda$ gives the sensitivity for changes in the constraint function is derived for the case $g(x)−h=0$ for varying $h$. Is there somewhere a reference deriving this for $g(x;h)=0$?
I looked through the literature and asked one expert. No trace of such a proof. But there must be one, I am sure.
I can do it myself, however, I would like to avoid to reinvent the wheel.
I am only looking for a hint for a reference, no explanations how to do it.