# Questions tagged [lagrange-multipliers]

The method of Lagrange multipliers finds critical points (including maxima and minima) of a differentiable function subject to differentiable constraints.

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### RSM and steepest ascent for new $x'$ coordinates

In Myers, Montgomery, & Anderson-Cook, C. M. (2016)$^1$ the authors provide (p. 235) a general methodology to find new $x'$ coordinates in the path of steepest ascent based on constrained ...
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### Gradient descent finds local minima for a problem that can be formulated as a convex problem

I am trying to find $$\min_W \|Y-XW \|_F^2$$ $$s.t. \exists ij, W_{ij}\geq0$$ where X is input data and Y is the output data we try to fit to. This is a convex optimization problem that can be ...
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### Extracting the value of the constraint given a known lambda parameter in LASSO

The LASSO problem is expressed as \begin{equation} \hat{\theta}\in \arg\min_{\theta\in\mathbb{R}^d} \left\{\frac{1}{2n}\lVert y-X\theta\rVert_2^2+\lambda_n\lVert\theta\rVert_1\right\} \end{equation} ...
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### Rewriting Lagrange Multiplier with non-linear optimization

NOTE: if you have access to the book mentioned below , please skip to the part of this post marked with (*), as I will now provide a short summary of the relevant background information for my ...
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### What is the maximum entropy distribution with a mean of 0, stdev of 1, skew of 1 (instead of zero), and kurtosis of 1 (instead of 3)?

As we know, there are an infinite number of distributions with mean of zero and variance of one. One of the special things about the normal distribution is that is has the maximum entropy. (https://...
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### How to solve MNP (minimum norm) problem in SVM?

I'm reading an article, which says that MNP (minimum norm problem) can be solved as SVM. In the minimum norm problem, we're given a set of points in $R^d$ and need to find a point in convex hull of ...
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### R built-in Breusch-Pagan Test getting different results from manual Calculation

I was using the following code to calculate the bp-test (eaef.csv can be found here). ...
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### ARCH effect - Conflicting Results from Lagrange Multiplier Test and Ljung Box Test?

I want to test for presence of conditional heteroskedasticity in a vector of ARIMA(0,0,0) residuals. For this purpose, I would like to see if both ARCH Lagrange Multiplier Test (on levels of ...
I have a forecasting problem and already built a decently working VAR model which provides forecasts as $\hat{Y}_{iT}$, for $i = 1,..n$ and $T$ is forecast time period. But now I have an additional ...