On a lecture note I read about Calculus of Variations
the author talks about Euler-Lagrange equation, then continues to say "unfortunately, many times a closed form solution [for EL eqn] is not known. One way to cope with this problem is to use a gradient descent technique. Incidentally, the left hand side of the Euler-Lagrange equation can be regarded as an infinite-dimensional gradient".
How did he make this transition, from a EL PDE to gradient descent? Which class, book would cover this subject? My books on Calculus of Variations have nothing on this. Should I look under Optimization, Numerical PDE?