Timeline for Euler-Lagrange equations and Bellman's principle of optimality
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Apr 12, 2016 at 20:43 | history | bounty ended | CommunityBot | ||
| S Apr 12, 2016 at 20:43 | history | notice removed | CommunityBot | ||
| Apr 11, 2016 at 19:19 | answer | added | Pait | timeline score: 0 | |
| Apr 11, 2016 at 18:14 | comment | added | john mangual | looking again at your question, there is nothing about discretization or dynamic programming except for Bellman's name. Perhaps I will read up and ask my own question 😯 | |
| Apr 11, 2016 at 17:17 | comment | added | Pait | Fascinating. If the papers suggested in the answers don't really solve the problem, perhaps I should assume that it is open. At least until the bounty expires ;-) | |
| Apr 6, 2016 at 13:51 | answer | added | homocomputeris | timeline score: 1 | |
| Apr 5, 2016 at 9:22 | history | edited | Pait | CC BY-SA 3.0 |
added 238 characters in body
|
| Apr 5, 2016 at 9:09 | comment | added | Pait | Perhaps a little confusion can arise at 1st glance from the fact that in the calculus of variations in several variables the letter $x$ is often used to denote the independent space variable ($u$ is often used for the dependent variable). Usually in dynamical programming the independent variable is time $t$, the dependent variable is state $x$, and in controls problems $u$ is the input. | |
| Apr 5, 2016 at 8:28 | answer | added | Carlo Beenakker | timeline score: 2 | |
| S Apr 4, 2016 at 18:54 | history | bounty started | Pait | ||
| S Apr 4, 2016 at 18:54 | history | notice added | Pait | Draw attention | |
| Mar 30, 2016 at 17:04 | comment | added | Pait | Yes, dynamic programming is an alternative to the calculus of variations, but as far as I know only for those problems in which the independent variable is 1-dimensional. Finding geodesics is an example of those. I am interested in minimizing $\int_{\mathcal X} L(u,p,x) dx$ with ${\mathcal X}$ a subset of $R^n$, for example, in which case I am only aware of the Euler-Lagrange approach. | |
| Mar 30, 2016 at 13:42 | comment | added | john mangual | Wikipedia does mention Dynamic Programming as an alternative to Calculus of Variations. I suspect when you try to discretize the Euler-Lagrange equation (e.g. find a geodesic curve on your computer) the algorithm you use involves some type of memoization or technique to keep things in memory. I don't know of any deep or profound uses of this equality between Principle of Least Action and Dynamic Programming. | |
| Mar 30, 2016 at 11:43 | history | asked | Pait | CC BY-SA 3.0 |