Dear all,

given a 2-D vector field V(x,y), I have to find the 2-D curve along which the path integral (integral of V.dl) is minimum, the starting and ending points being fixed. It can be assumed that V(x,y) is infinitively differentiable, but not much more.

According to what I read, I think -- but I'm not sure -- that a generalized gradient descent or Newton method could work, with the gradient replaced by the Gateaux or Fréchet derivative of the functional... However, I haven't found yet a good reference (book or scientific paper) that really details the implementation of such a method. For example, the derivative of a functional being itself a functional, I don't really see how to use it in the methods...

Do you have an advice? Or a good reference I should read?

Thanks,

Bruno G.

Hi nono,
The problem you mentioned falls under the general class of variational problems.

Read books (or tutorials from the internet) on variational methods.

Good luck