# Sensitivity Lagrangian solution general case

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.

• If I remember correctly then Nocedal and Wright's book Numerical Optimization contains a proof or a reference to the proof. – dweber Sep 17 '18 at 17:40
• Only for the linear case unfortunately. – Karl Sep 17 '18 at 17:41