I agree with your comments about F. But I am still reticent about editing the page. Are you willing to make the necessary changes to your caveat section? RE my article: thanks for the tip on protocol. If and when the blasted thing ever appears, assuming I remember, I will post something to the talk page for the article.
Lagrange Multipliers Caveat Response
I am a little uncomfortable editing pages here, even though you suggest I undo your change. I am not familiar enough with the conventions and what not. For example, is this the right way to have an exchange? Posting comments to one another's talk pages? Is there a more efficient way? Something with threaded discussions?
From what I have seen, there is a common misconception that F (not f) does indeed take a maximum or minimum at the solution of the original optimization problem. So I would not want to completely delete your caveat. But it might more correct if it said something along these lines: Be aware that the solutions are stationary points of the Lagrangian F, and are generally saddle points of F, not maxima or minima. [a reference can be added to my paper after it appears]. Even considering F as a function of x and y alone, and holding constant at , need not be a maximum or minimum. As we shall see below, under certain stronger assumptions, the strong Lagrangian principle holds ... . Calqtopia (talk) 22:49, 23 December 2008 (UTC)
Lagrange Multipliers Caveat
On the Lagrange_multipliers page, the caveat about local and global extrema of F is not quite correct. Except for the singular cases (where grad g is zero or undefined), the stationary points of F are ALL saddle points. This is apparently pretty well known to specialists in constrained optimization or nonlinear programming or whatever it should be called, but not very well known to general math types.
Even for the strong Lagrangian principle, I don't think that the Lagrangian can have a global maximum, but I don't know what Slater's condition is, so I may be mistaken.
I have a paper coming out in Math Magazine in a few months that gives the details of the assertion above. So, I am not sure whether it makes sense to modify the wiki entry now, or wait until the reference can be included. Calqtopia (talk) 14:55, 18 December 2008 (UTC)
- See your talk page for my reply.
Hi Simplifix, I hope that you are well. Thanks for your additions to the Milnor number article. I agree that something should be added about the vanishing cycles on the Milnor fibre. Perhaps you would like to do this? I see that you have also created an article on contact equivalence. I'm guessing that you work in singularity theory. Might I ask who you are? I'm Declan Davis and my PhD supervisor was Peter Giblin at Liverpool. I'm just wondering if I might actually know you under your real name. Δεκλαν Δαφισ (talk) 18:27, 9 November 2008 (UTC)
- 3(x2 + y2)
- 3(x2 + y2)
- 3 - 5
- 3 − 5
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