Re: Calculus of variations vs. continuous-time dynamic programming

On Apr 12, 3:15 am, Dong Ta <dongta....@xxxxxxxxx> wrote:
It's my observation that when dealing with an optimization problem
(optimization of a function), physicists tend to use calculus of
variation while people in Economics and Finance tend to use
continuous-time dynamic programming.

I assume by continuous-time dynamic programming you mean solving the
Hamilton-Jacobi-Bellman (or Riccati) equation.

How do you compare the 2 approaches? What are the pros and cons?

Solving the HJB gives you feedback controls. This gives more robust
controllers but also sometimes more clue about the behaviour of the
controller. However, solving the HJB is hard even numerically. Even
with a moderate-sized nonlinear system you probably have to contend
with open loop solutions found by calculus of variation techniques.

As for the general question "why people in field X use method Y and
not method Z", the answer is usually "because the guy who did it first
used X".

.

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