Hey friends, I have often seen many brilliant solutions, featuring Lagrange Multipliers and think that they are of much use to compute maxima and minima. But I know nothing about them. So please can anyone suggest me sources about Lagrange multipliers? And any more works by Lagrange with a light description 'bout them. Thanks in advance.

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TopNewestI found Lagrange multipliers to be suspicious back when I could have learned them for the first time, so I didn't learn them and always took a way around them.

Some years later I started scribbling on a napkin trying to figure out how I would look for constrained minima and realized what I was writing down had the same form as Lagrange multipliers.

I wrote the following to myself to remember the argument:

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Thanks, now can you suggest me a source, which demonstrates cool lot of examples about this tool?

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Looks like I'll leave Lagrange Multipliers alone until later, no matter how useful they are to my inequalities studies.

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After a while, Lagrange becomes the "default" approach for constrained inequality. Economists use it almost exclusively, and jump immediately to the Kuhn-Tucker conditions.

Be warned though, as with all approaches, you need to understand when it applies, and the various pitfalls. Very often, people fail to properly consider the boundary, especially on an unbounded domain.

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Basically if you're given a constraint \(g(x_1,x_2,\dots,x_n)=k\) and you want to maximize \(f(x_1,x_2,\dots,x_n\), then it occurs where \(\nabla f(x_1,x_2,\dots,x_n)=\lambda\nabla g(x_1,x_2,\dots,x_n)\). If you're not familiar with \(\nabla f(x_1,x_2,\dots,x_n)\), it's just a vector containing its partial derivatives: \(\nabla(5xy+z^3)=\left<5y,5x,3z^2\right>\). So the strategy is to find \(\lambda\) or find some conditions for your variables using that proportion.

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