I'm currently reading the "Pattern Recognition and Machine Learning" book by Chris Bishop. And I'm having trouble understanding how they introduce Lagrange multipliers in Appendix E.
It explains that some constraint function, g(x), where x is a vector, can be represented geometrically as a constraint surface in x space. However, it then goes on to say that the constraint function g(x) = g(x + e), where x + e is a nearby point. How does that work? Wouldn't a slightly different point produce a different output? Or is it saying that it is approximately the same?
The book is available as a free PDF online.