hey just a heads up I think at 27:30 you meant to make it equal to 0 as log(1) = 0, might want to put up an annotation. Otherwise great video I would love to see more content like this!
Hi Ahmad, thank you for the great content! I dont understand something - the log function is concave, not convex.. I mean, does it make any difference? because we want to minimize the objective
Hey Yuval, yes you are right, log(x) is concave in x and hence - log(x) is convex. Of course there is a difference. Imagine minimizing a convex function x^2 vs minimizing a concave function -x^2.
@@AhmadBazzi thanks for the quick reply! if so, I still don't understand how this logarithmic trick is working for GP.. because we are using log, not -log, and we are saying that it is convex..
@@AhmadBazzi at 27:40 you say that the objective and the inequality functions are convex, but they are logs of something so they are concave, not convex.. thats why I asked if there is any difference - and if there is - I dont understand why it is said these logs are convex.
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That intro was really improved! Thanks for this lecture!
You're very welcome!
hey just a heads up I think at 27:30 you meant to make it equal to 0 as log(1) = 0, might want to put up an annotation. Otherwise great video I would love to see more content like this!
Hi Ahmad, thank you for the great content!
I dont understand something - the log function is concave, not convex.. I mean, does it make any difference? because we want to minimize the objective
Hey Yuval, yes you are right, log(x) is concave in x and hence - log(x) is convex.
Of course there is a difference. Imagine minimizing a convex function x^2 vs minimizing a concave function -x^2.
@@AhmadBazzi thanks for the quick reply! if so, I still don't understand how this logarithmic trick is working for GP.. because we are using log, not -log, and we are saying that it is convex..
Kindly pinpoint what has not been understood.
@@AhmadBazzi at 27:40 you say that the objective and the inequality functions are convex, but they are logs of something so they are concave, not convex.. thats why I asked if there is any difference - and if there is - I dont understand why it is said these logs are convex.
No you are wrong. log(sum of exponentials) is convex not concave in x_1...x_n. This is not to be confused with log(x).
Can you please also add the links for the relevant papers as well?
Hey Hamza, will do on the upcoming website.
I saw your other comment on the website. I’m working on it. Hopefully it would be ready in a month or two something like that :)