Re: Calculus of variations vs. continuous-time dynamic programming
- From: quasi <quasi@xxxxxxxx>
- Date: Wed, 11 Apr 2007 22:13:33 -0500
On 11 Apr 2007 18:49:11 -0700, "C6L1V@xxxxxxx" <C6L1V@xxxxxxx> wrote:
On Apr 11, 5:15 pm, Dong Ta <dongta....@xxxxxxxxx> wrote:
Hello,
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.
How do you compare the 2 approaches? What are the pros and cons?
I once attended a seminar by Frank Clarke, who said that the
difference between Calculus of Variations and Optimal Control is that
in the former the control vartiable lies in an open set but in the
latter it lies in a closed set. I did not fully understand his remark.
R.G. Vickson
I'll guess that the implication is this:
In Calculus of Variations, you first try to insure that the feasible
domain is an open set. Hence, the theory is simpler both with respect
to the problem of proving the existence of an optimal solution and
also with respect to the problem of finding one.
In Optimal Control, the solution often involves extreme values of one
or more of the control variables. Thus, the feasible domain is
typically a closed set, and an optimal solution will often lie on the
boundary.
Just a guess (but I like to make guesses).
quasi
.
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