Is There an Alternative Method to Obtain the Extremum of a Functional?

[eljose]

Let,s suppose we have a functional J and we want to obtain its extremum to obtain certain Physical or Math properties:

$$\delta{J[f(x)]}=0$$

Yes you will say to me " You can apply Euler-Lagrange Equation to it and generate a Diferential equation to obtain f"..of course is easier saying than doing..in fact for simple calculus of minimizing a function for example:

$$g(x)=cos(x)+x^{2}$$ you get $$sen(x)=2x$$

of course you can,t solve the last equation "exactly" so you have to make some approach to it either iteratively or another method, my question is if to obtain the extremum of g(x) there is an iteratively method and if there is another method to obtain the extremum of a functional appart from using Euler-Lagrange equations..thanks.

 

[fresh_42]

This depends on the situation. In the generality you asked, it will be difficult to find another answer than yours. One idea could be to find a basis and use a Simplex algorithm.