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Hi,
I just changed looking for an extremum of g to looking for an extremum of h although I'm not absolutely sure. But I think it is the right term.
Citation from the article: "One may reformulate the Lagrangian as a Hamiltonian, in which case the solutions are local minima for the Hamiltonian. This is done in optimal control theory, in the form of Pontryagin's minimum principle." This seems a very important statement, and the article should include detailed explanations and an example of such transform "Lagrangian to Hamiltonian". Links here redirect to general theory of Hamiltonian dynamics and do not explain how this reformulation can be done
Video 27.62.210.24 ( talk) 15:48, 14 October 2022 (UTC)
The section Modern formulation via differentiable manifolds contains the following sentence:
"In what follows, it is not necessary that be a Euclidean space, or even a Riemannian manifold."
But it is not stated what is necessary for to be.
I hope someone knowledgeable about this matter can fix this, by stating some reasonable condition(s) that must satisfy.
Surely it must satisfy *some* condition(s) for these operations to make sense.
I guess that in the last equation in the Statement section, either the left- or the right-hand side should be negated, otherwise x* is not a solution. Should be: D f(x*) = -λ*ΤD g(x*). Павел Кыштымов ( talk) 21:17, 19 December 2023 (UTC)
This
level-5 vital article is rated B-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
Daily pageviews of this article
A graph should have been displayed here but
graphs are temporarily disabled. Until they are enabled again, visit the interactive graph at
pageviews.wmcloud.org |
Hi,
I just changed looking for an extremum of g to looking for an extremum of h although I'm not absolutely sure. But I think it is the right term.
Citation from the article: "One may reformulate the Lagrangian as a Hamiltonian, in which case the solutions are local minima for the Hamiltonian. This is done in optimal control theory, in the form of Pontryagin's minimum principle." This seems a very important statement, and the article should include detailed explanations and an example of such transform "Lagrangian to Hamiltonian". Links here redirect to general theory of Hamiltonian dynamics and do not explain how this reformulation can be done
Video 27.62.210.24 ( talk) 15:48, 14 October 2022 (UTC)
The section Modern formulation via differentiable manifolds contains the following sentence:
"In what follows, it is not necessary that be a Euclidean space, or even a Riemannian manifold."
But it is not stated what is necessary for to be.
I hope someone knowledgeable about this matter can fix this, by stating some reasonable condition(s) that must satisfy.
Surely it must satisfy *some* condition(s) for these operations to make sense.
I guess that in the last equation in the Statement section, either the left- or the right-hand side should be negated, otherwise x* is not a solution. Should be: D f(x*) = -λ*ΤD g(x*). Павел Кыштымов ( talk) 21:17, 19 December 2023 (UTC)