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

In Lecture 3 of this course on convex optimization, we will be covering important points on convex functions, which are the following:

00:00:00 Intro
00:01:14 Definition of Convex Function
00:03:31 Examples of Convex Function
00:13:50 Convexity in Higher Dimensions
00:24:30 First-order Condition
00:27:08 Second-order Conditions
00:35:17 Epigraphs
00:37:25 Jensen's Inequality
00:39:49 Operations preserving Convexity
00:52:21 Conjugate Convex function
01:02:09 Quasi Convex functions
01:11:14 Log-Convex functions
01:16:16 Convexity with respect to generalized inequalities
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References:
[1] Boyd, Stephen, and Lieven Vandenberghe. Convex optimization. Cambridge university press, 2004.
[2] Nesterov, Yurii. Introductory lectures on convex optimization: A basic course. Vol. 87. Springer Science & Business Media, 2013.
Reference no. 3:
[3] Ben-Tal, Ahron, and Arkadi Nemirovski. Lectures on modern convex optimization: analysis, algorithms, and engineering applications. Vol. 2. Siam, 2001.
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Instructor: Dr. Ahmad Bazzi
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Credits :

#ConvexOptimization #Convex #Functions

[truckdriver]

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

[kphrrkv]

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

[kritbalwani]

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[DedeIkrom]

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

[yalamff]

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

[ussoperativeangel]

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

[jrsavage]

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 👍👍

[ramsajiwan]

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

[detectivespot]

Thank you so much for the video! This is a small but high-quality channel!

[frokxjm]

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

[tarlanheydarov]

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

[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.

[anuowolabi]

This is so useful, thank you so much

[kursat]

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

[enesyt]

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

[niajsaisasaas]

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

[Betweenthelines]

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

[alperengunes]

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

[pubg_tr]

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!

[nathanpark]

highly highlu underrated channel and videos