MHB What is the Hessian method for determining concavity/convexity?

  • Thread starter Thread starter OhMyMarkov
  • Start date Start date
  • Tags Tags
    Hessian Test
Click For Summary
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.

PREREQUISITES
  • Understanding of Hessian matrices
  • Knowledge of eigenvalues and eigenvectors
  • Familiarity with partial derivatives
  • Basic concepts of concavity and convexity in calculus
NEXT STEPS
  • Study the properties of Hessian matrices in detail
  • Learn how to compute eigenvalues and eigenvectors using tools like NumPy
  • Explore applications of concavity and convexity in optimization problems
  • Review multivariable calculus concepts related to second-order derivatives
USEFUL FOR

Students and professionals in mathematics, economics, and engineering who are involved in optimization and require a solid understanding of concavity and convexity in functions.

OhMyMarkov
Messages
81
Reaction score
0
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!
 
Physics news on Phys.org
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.
 

Thread 'How does this derivative work? And why the speed of light remains?'

Relativistic Momentum, Mass, and Energy Momentum and mass (...), the classic equations for conserving momentum and energy are not adequate for the analysis of high-speed collisions. (...) The momentum of a particle moving with velocity ##v## is given by $$p=\cfrac{mv}{\sqrt{1-(v^2/c^2)}}\qquad{R-10}$$ ENERGY In relativistic mechanics, as in classic mechanics, the net force on a particle is equal to the time rate of change of the momentum of the particle. Considering one-dimensional...
View full post »

Similar threads

Stationary points classification using definiteness of the Lagrangian
  • · Replies 4 ·
Replies
4
Views
2K
What Is the General Form of the Third Partial Derivative Test?
  • · Replies 1 ·
Replies
1
Views
4K
Is f(x,y) = (x^2) * exp(y) a convex or concave function?
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Hessian of least squares estimate behaving strangely
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Correlation between parameters in a likelihood fit
  • · Replies 3 ·
Replies
3
Views
2K
MHB Help with calculus problem with logarithm base e
  • · Replies 5 ·
Replies
5
Views
3K
Q on Second partial derivative test for functions of n variables
  • · Replies 2 ·
Replies
2
Views
3K
Function in 3 variables, determinant of the Hessian=0
  • · Replies 1 ·
Replies
1
Views
3K
Graphing Derivatives: Concavity and Inflection Points
  • · Replies 4 ·
Replies
4
Views
3K
MHB Power Series (Which test can i use to determine divergence at the end points)
  • · Replies 1 ·
Replies
1
Views
2K