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Here is the problem

What I attempted was calculating the Hessian and trying to prove that it's positive definite/semi-definite or negative definite/semi-definite. It doesn't seam to work as I am getting that the second order principle minor can be both negative and positive which would suggest that this function is neither convex nor concave.

Ruben Shahnazaryan
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  • Welcome to Math.SE. Can you please edit your post and write down the problem using LaTeX / MathJax, or, at least, add an ! right before the image link to make the image appear? See also some formatting help. – Ertxiem - reinstate Monica May 15 '19 at 11:28
  • Furthermore, it would increase the likelihood of getting an useful answer if you were more specific, for instance, writing down in your post the steps you did to solve the problem. Sometimes, we all make small mistakes in the computations. See some tips on how to ask – Ertxiem - reinstate Monica May 15 '19 at 11:28
  • Thanks for the tips :) I'm quite new here at it seems like the ! command is for those with at least 10 rep. I actually tried writing this problem using MathJax, and did look at the links you've sent before uploading. I literally spend an hour trying to write a function and just gave up. – Ruben Shahnazaryan May 15 '19 at 12:16
  • Please, don't use images as main content of your post. This makes your question impossible to search and inaccessible to the visually impaired. Please transcribe text and mathematics (note that you can use LaTeX) and don't forget to give proper attribution to your sources. – Pantelis Sopasakis May 15 '19 at 13:00
  • Formatting tips: $$f(x_1, x_2, x_3) = x_1^2 + x_1^2 x_2^2 + x_2^2 + e^{x_3^2}$$ is obtained with $$f(x_1, x_2, x_3) = x_1^2 + x_1^2 x_2^2 + x_2^2 + e^{x_3^2}$$, and $\mathbb{R}^3$ is obtained with $\mathbb{R}^3$. – Ertxiem - reinstate Monica May 15 '19 at 13:07
  • Thanks a lot Ertxiem. From now on I will use that. Could you tell me where you can learn all the syntax? it seams like the basic tutorial and quick reference does not have everything. – Ruben Shahnazaryan May 15 '19 at 13:37
  • Some functions are neither convex nor concave. – Mark L. Stone May 15 '19 at 23:49

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