Talk:Lagrange multiplier

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Notation change[edit]

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.

Thanks for catching that; that occurrence of g seems to have been missed when the notation was changed in December.--Steuard 20:51, Jan 28, 2005 (UTC)

Strictly looking for an extremum of

h({\vec {x}},{\vec {\lambda }})

also implies the original

{\vec {g}}({\vec {x}})={\vec {0}}

via

{\frac {\partial {\vec {h}}}{\partial {\vec {\lambda }}}}={\vec {0}}

. 84.160.236.56 19:29, 6 Feb 2005 (UTC)

Reformulating Lagrangian as Hamiltonian[edit]

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

Real analysis Lagrange multiplier method[edit]

Video 27.62.210.24 (talk) 15:48, 14 October 2022 (UTC)[reply]

Puzzling assertion[edit]

The section Modern formulation via differentiable manifolds contains the following sentence:

"In what follows, it is not necessary that $M$ be a Euclidean space, or even a Riemannian manifold."

But it is not stated what is necessary for $M$ to be.

I hope someone knowledgeable about this matter can fix this, by stating some reasonable condition(s) that $M$ must satisfy.

Surely it must satisfy *some* condition(s) for these operations to make sense.

Wrong sign in the Statement section[edit]

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)[reply]