I have asked this question already on maths and mathoverflow.

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.

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

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.