Convex Functions: Info on Minima, Reconstructing Original Functions

[moyo]

If you would allow me to ask...

if i have two convex functions , and i was to place one inside the other, i.e. convolute them...what could be said in general about the resultant function.

what information about the original functions can be taken from the positions of the minima.

and is there a way to reconstruct the original functions if given only the graph of their composition.

Thankyou

 

[jvicens]

for your question! The resulting function from convoluting two convex functions will also be a convex function. This is because the sum of two convex functions is also convex.

The positions of the minima can provide information about the structure of the original functions. For example, if the minima of the resulting function occur at the same positions as the minima of one of the original functions, it could indicate that the other original function is relatively flat in that region.

However, without knowing the specific equations of the original functions, it may not be possible to fully reconstruct them from just the graph of their composition. This is because there could be multiple combinations of functions that could result in the same graph when convoluted.

In order to fully reconstruct the original functions, you would need more information such as the specific equations or additional data points. I hope this helps answer your questions!