What is the Hessian method for determining concavity/convexity?

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SUMMARY

The Hessian method is a definitive technique for determining the concavity or convexity of a function. This involves calculating the Hessian matrix, which is the square matrix of second-order partial derivatives. To assess concavity, one examines the eigenvalues of the Hessian; if all eigenvalues are positive, the function is convex, while negative eigenvalues indicate concavity. This method is essential for optimization problems in multivariable calculus.

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  • Understanding of Hessian matrices
  • Knowledge of eigenvalues and eigenvectors
  • Familiarity with partial derivatives
  • Basic concepts of concavity and convexity in calculus
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  • Learn how to compute eigenvalues and eigenvectors using tools like NumPy
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OhMyMarkov
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Hello Everyone!

I'm trying to remember a quick method for determining whether a function is concave or convex. There was something that involved finding the Hessian of the function, and then looking at the diagonal elements, then, I completely forgot...

What's the rest of this method, I don't remember I even had to find the eigen values...

Thanks!
 
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OhMyMarkov said:
Hello Everyone!

I'm trying to remember a quick method for determining whether a function is concave or convex. There was something that involved finding the Hessian of the function, and then looking at the diagonal elements, then, I completely forgot...

What's the rest of this method, I don't remember I even had to find the eigen values...

Thanks!

Hi OhMyMarkov, :)

The method of using the Hessian of a function to determine the concavity/convexity is described >>here<<.

Kind Regards,
Sudharaka.
 

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