Can Gradient Descent be applied to a functionals?

31 Views Asked by At

If the calculus of variations is the optimization of a functionals. What are the methods for optimize this functionals? is the Gradient Descent algorithm useful for optimize functionals?

I research here and there is a question related to this here the user @copper.hat said:

Gradient descent is for unconstrained problems, your space of valid s is not even convex. Without additional assumptions the best we can hope for by way of convergence for unconstrained gradient descent in ℝ is that accumulation points are critical points.

I really can't understand that statement I know more calculus than calculus-of-variations. I would like a intuitive summarized answer about this. my question is:

  • Is Gradient Descent Useful for Calculus of variations?