Practice question · Multiple choice
Ordinary optimisation asks 'which price?' and calculus of variations asks 'which path?'. What kind of object is being differentiated in the second case?
Hints
- The input to the objective is not a number. What is it?
- Ask what you would perturb to test whether the path is optimal.
Show the answer
B. A functional, which scores an entire function with one number
Why
The input is a whole function and the output is a single score, so the perturbation is a wiggle in the path itself, that is what makes the Euler–Lagrange equation a differential equation rather than a formula. Option 3 is the discrete approximation, which is how it is usually computed.
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