# Questions tagged [lagrange-multiplier]

This tag is for the questions on Lagrange multipliers. The method of Lagrange multipliers (named after Joseph Louis Lagrange) provides a strategy for finding the local maxima and minima of a function subject to equality constraints.

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### How to solve the following convex optimization problem to get a closed form solution?

Please, can you help to solve the following convex optimization problem to get a closed-form solution? I tried to solve it using Lagrange multiplier but it's not easy. I can't get the closed-form ...
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### How to find the general form of minimum distance from the point (m,n) to the ellipse by using Lagrange Multiplier?

Excuse me! I have tried to solve this problem for a long time but I have stuck in this step. This is my work picture01. This is my work picture02. I cannot simplify y in term of a b m and n. It’s too ...
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### KKT and Constraint Qualification

Have studied lagrangian and optimization primarily via Khan academy, as got bogged down with Simon and Blume Mathematics for Economists/Chiang and Wainwright Fundamental Methods of Mathematical ...
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### Question about using Lagrange mutipliers finding the solution of PCA

I'm trying to use Lagrange mutipliers to find the solution of PCA. Assume the data matrix is X $= [X^{(1)},\dots, X^{(m)}] \in \mathbb{R}^{k \times m}$($k$ features and $m$ observations, already zero-...
Let $x,y$ and $z$ be the interior angles of a triangle. Suppose that $f(x,y,z)=\sin(x)\sin(y)\sin(z)$. Using the Lagrange multipliers, I know $f$ has a local maximum at $x=y=z=\pi/3$. However, I do ...