I heard a lot about the interpretation of Lagrange multipliers and the constraints qualification for the resolution of NLP but I still have a question:
Could we qualify the difficulty of solving a NLP based on the values of the Lagrange multipliers at the solutions?
In other words, could we say that a given NLP1 was more difficult to solve that NLP2 if for example max(Lagrange multipliers in 1)> max(Lagrange multipliers in 2)??
This question is motivated by a paragraph talking about sensitivity in the book numerical optimization of Nocedal.