Lecture 3 | Convex Functions | Convex Optimization by Dr. Ahmad Bazzi

[@nathanpark2665]

highly highlu underrated channel and videos

[@يومياتأطفالفيالحظر]

deserves big applause!! very informative in the smoothest way possible.

[@kritbalwani9121]

Im a newbie to convex opt and this video sure made things less shaky in my brains.I have a feeling in my gut telling me you are a fellow Moroccan. if so, bghit ghir ngol tbarklah 3lik et bonne continuation.

[@truckdriver5071]

Yes! Thank you! I will add a note in the video description

[@DedeIkrom97]

I took a class that I am not ready for and your videos have absolutely rescued me 😂

[@lglgunlock]

Hi, Dr. Bazzi, at 19:24, to prove g(t) is a convex function, we should first prove dom(g) is a convex set for any X and V, I think it is not obviously a convex set.

[@danmcgloven8169]

this is precisely what the theorem is saying, you do not need to worry about x and v. as long as x is in dom(f) for all v in R^n, then g(t) is convex.

[@ussoperativeangel1223]

After Stanford's Stephen Boyd's original lecture, this is most well explained content of Convexity Optimization, Thanks for doing beautiful work!

[@anuowolabi9602]

This is so useful, thank you so much

[@AhmadBazzi]

Glad you found it useful, Anu !!

[@yalamff1819]

Thank you for watching so attentively! Nice catch, b should be of size 1xm, and A should be of size nxm.

[@enesyt796]

I just checked the description, and i think the answer is blender. Thanks for the great work!

[@alqedra8]

Great to hear, thanks!

[@alperengunes7710]

Great explanation and animation! I wish you could do more optimization videos!

[@عبدالوهابفوزى-ث8ط]

I hope you continue this course. It's very useful and you are great. keep going on

[@AhmadBazzi]

Yes I will continue at a rate of 1 video per week, roughly speaking.

[@farahkmneimneh]

Thank you for the effort

[@AhmadBazzi]

glad you found it useful !!

[@niajsaisasaas]

How does the choice of variables and constraints affect the convexity of a function, and what considerations should be made when selecting them?

[@salahiddinaltahat1749]

Many thanks for your effort. just small note: at minute 33:00 -> partial derivative w. r. t. y is (-x^2/y^2), there should be no "2"

[@AhmadBazzi]

You are welcome. Indeed, you are right !!

[@Scott_Raynor]

@@AhmadBazzi Also the top left second derivative should be 2/y, not 2/y^2, no?

[@gwendolyngunnar4899]

@Scott no incorrect

[@jrsavage3111]

Wow I took this course last year, you covered a lot of material in such a short time. It is amazing, I hope all of the courses could be made in form of such high quality videos someday. Great work 👍👍

[@ramsajiwan6060]

Check out Constantine Caramanis too, he has such a firm grasp of the topic and he's really got those teaching skills

[@seydiozturk3141]

Glad to hear it!

[@ortayakarsk3460]

Awesome, thank you!

[@criticaltesisatc4045]

Good to hear :D

[@pubg_tr2308]

I should have made it more explicit, but for me “feasible region” is the same thing as “feasible set”, which is the set of the “x”s that we are allowed to pick. Great question!

[@nd-tech2456]

Helped a lot in econ class thanks

[@MRBEASTFAN1102]

Keep it up. But would be great if you work on audio quality as well.

[@barbiedunyasi3630]

wonderful presentation

[@SHARMAX_YT]

This series is absolutely formidable. thank you!

[@tarlanheydarov]

What are some common challenges or limitations to working with convex functions, and how can they be addressed?

[@zahid1967]

got here from a reddit post :) this is so cool man!

[@kursat3390]

What are the benefits of working with convex functions in optimization and other mathematical applications?

[@beleskoleler]

Bravo my friend, you are a star. This content is superb!

[@iclaliremuslu7374]

Thanks Mr Ahmad, appreciate it ;)

[@dorukveoguzdgdfgdfg6242]

Very nice, well done

[@Betweenthelines366]

What is the difference between a strictly convex function and a strongly convex function, and how do these concepts affect optimization performance?

[@taniyasambyal3607]

Thank you! Cheers!

[@hermoine6625]

Excellent material - I've seen a few so far. Only thing I'd quibble with is that your linear regression example has a square matrix A so (obviously) it's only an optimization problem if the rank is deficient. I'm an expert in solving linear programming problems BTW

[@prasaddate894]

great effort thanks

[@xizzziz]

This is amaizing !!!

[@hbasu8779]

HI Ahmad, Thank you very much for explaining everything so well. I have one question though. At around 1:11:30 you have a staement written on your notes : log f(x) is convex (or concave) when f(x) is convex (or concave). This does not sound correct. Becuase f(x) = x^2 is convex while log f(x) = 2 log x is not. Can you please comment on this?

[@hbasu8779]

@ONENESS_ALL_THE_TIME Okay. Thank you for responding to this.

[@EarningTechnology]

More is coming very soon, stay tuned!

[@dragonteam2532]

Thank you so much!

[@habiptatlibulak]

How can you determine whether a given function is convex, and what methods or tools are commonly used for this purpose?

[@lulu-ti1rn]

Great series! Could you tell me what tool you use for neat animations like this?

[@HuSoUyGaR]

What is a convex function, and what are its properties?

[@huseyinhatip7066]

Do i understand you right: feasible set is the set of those x that we can pick considering our constraints, feasible region is the set of all f(x) that we can get ?

[@urdupoetrytreasure7855]

cool explanation😁

[@superheromovieclip5038]

Awesome lecture. What software did you use to create these animations?

[@DrBilalHussain]

18:19: I have written the following code but there seems to be an error. Any suggestion? [X,Y] = meshgrid(0:0.1:5, 0:0.1:5); Z = log(X.^2 - Y.^2); for k = 1:size(Z,1) for m = 1:size(Z,2) if(X(k,m) > Y(k,m)) Z(k,m) = log(X(k,m)^2 - Y(k,m)^2); end end end surf(X,Y,Z) % Equivalent to plot in 3D Error using surf (line 71) X, Y, Z, and C cannot be complex. Error in All_Codes (line 74) surf(X,Y,Z) % Equivalent to plot in 3D

[@TAFUTUBE]

Nice work!

[@factifiedindia9141]

Nice explanation

[@orucoruclu3702]

Really nicely done. Sorry to come off as complicated, but could I persuade you to reupload your videos without the music in the background. I feel it is super distracting.

[@neptune6k]

very good....thank u

[@angelofdeath6813]

Thank you!

[@muyaz9369]

Thanks! 😃

[@choking4900]

59:05 I can't understand the Conjugate Convex function. when f(x) = |x| why the value is 0, where -1 < y < 1. I know that is not a distance, But I don't know what is it. Can you explain what it is?

[@AhmadBazzi]

Hello 초킹네, thanks for your question. As you can see, the conjugate is defined as the supremum over real x of the function yx - f(x). Now looking at the figure 59:05, the maximum "signed distance" is 0, which occurs at x = 0. Any other choice of x will leave yx - f(x) negative for -1 < y < 1. I hope this clarifies.

[@guptariya43]

@ 26:56 is that a taylor series ?

[@AhmadBazzi]

Yes Riya, you are right. This is a multivariate version of Taylor series.

[@ozcnyorm]

Thanks a lot!

[@matthewygf]

Still super useful in 2021

[@filoking9824]

The intro is way too long, but the blender animations are so satisfying!

[@osman25887]

How can you use convex optimization to find the global minimum of a convex function?

[@557_tycs_anuragjaiswar5]

What software did you use to create the examples?

[@everydaynewchallenge2927]

is the is log (1 + exp(wT xi)) for w ∈ Rd convex and why ?

[@gorkemkaya4878]

Thanks for the feedback?

[@chilldown9778]

Excuse me, could you explain it to me in details about the 2nd conditions of functions can be called convex? why the "shuttle(idk what it is,I just write the same as the subtitle)" is between 0 and 1? Lastly, what's the meaning of shuttle in the functions, I mean why we need them to define convex function? Thank you in advance..

[@darrirro]

Hi man, Do you happen to have solved exercises on this chapter?

[@ersancive6949]

waiting for more vids ;)

[@adanesh]

there is no voice at 1: 06: 00. How s(alpha3) is convex?

[@AhmadBazzi]

Hi Ali, thanks for the note. The microphone back then was just a mess. Fortunately, I've managed to change it. It's convex because S(alpha3) is nothing other than the set { x < x3 } which is a "continuous 1D set", hence convex. NOTE: THIS IS NOT AN EPIGRAPH. IT IS NOT THE RED 2D REGION YOU SEE IN THE ASSOCIATED CURVE, WHICH IS CLEARLY NOT CONVEX.

[@عبدالوهابفوزى-ث8ط]

There are some problems in voice. the videos become silent in many instances

[@AhmadBazzi]

yes I agree .. really sorry for the inconvenience.. will do my best to avoid these issues in the future !!

[@rakeshkumarbiswal9489]

sir plz uplode the notes

[@AhmadBazzi]

Hello Rakesh, I’m planning to host a website soon where i’ll have all the equations and notes written and formatted clearly. Thank you for following the channel. Make sure you subscribe and hit the notification button to receive the most recent updates about the channel :)

[@boothamgaming123]

Manim, blender3d, and adobe premiere

[@miaboruto7091]

prove that f(z) = 1/((z + 1)(z - 1)) 1/3 * sum ((- 1) ^ n * (r * u ^ n))/((z - 2) ^ (n + 1)) has power series as the formula؟

[@tahseensaad7860]

Hi sir, please can I have your email address I have questions regarding to convex Opt problem?

[@AhmadBazzi]

Hello Tahseen. It is recommended that you ask the question in the comment section so that other viewers who have similar questions could profit from yours.

[@tahseensaad7860]

Thanks for the late reply so fast 3 months !!!! Some questions cannot be asked in comment section. Since 3 months ago questions, I can't remember what I was asking about.

[@ardademir3593]

Thanks a lot!!