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?