# 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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### Strange constraint in optimization problem

I am trying to solve the following QP : $$\min_{x} \quad (1/2)\|y - Ax \|^2 _2 + \lambda \|Dx\|_1$$ where $y \in \mathbb{R}^n$, $A \in \mathbb{R}^{n\times m}$, $D \in \mathbb{R}^{l\times m}$. Assume :...
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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://...
27 views

### 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 ...
38 views

522 views

### 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). ...
703 views

### 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 ...
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### Scaling prediction from VAR model subject to a equality constraint

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 ...
658 views

### Number of lags to use in Engle's ARCH-LM test [duplicate]

How does one decide on number of lags to use in this test? Can one just justify the number based on previous papers? To clarify, I am forecasting conditional variance, and have generated my log ...
453 views

### Can I use a spatially lagged Dependent Variable while using Spatial Error Model?

I have following issue: I run spatial diagnostics on dependencies for my Log-Log Transformed regression model. LM Tests (including Robust) are highly significant. Since I am using GeoDa, I cannot ...
327 views

### SVM - Reason for using Lagrangian Dual [duplicate]

Objective To confirm if the understanding is correct regarding the reason why Lagrangian Dual is used in SVM. Background While Machine Learning, gradient descent is used at regression, logistic ...
895 views

### KKT in a nutshell graphically

Objective Confirm if the understanding of KKT is correct or not. Seek for further explanation and confirmations on KKT. Background Trying to understand KKT conditions, especially the complementary ...
I am beginner learning Lagrange multipliers with wiki article. Consider: maximize $f(x,y)$ subject to $g(x,y) = 0$ I understand that to maximize I must follow the gradient $\nabla {_{x, y}}^{}f$. I ...