Lecture 7 | Quadratically Constrained Quadratic Programs | Convex Optimization by Dr. Ahmad Bazzi

[@karannchew2534]

Hi Dr Bazzi, Some feedback if you don't mind, for improving 'watchability: 1) please refrain from moving around the pointer unnecessarily, it's distracting; 2) please avoiding switching between windows too frequently; 3) the writing/drawing often suddenly jump forward (like auto-complete effect), please avoid or less frequently please; 4) if you use a mouse to write, perhaps consider using a pencil, to improve readability. Thanks for the excellent videos. Will come back for more!

[@AhmadBazzi]

Hello Kar, thanks for all the remarks. They were really helpful. I am taking them into account in my new videos. Please check them and let me know :)

[@karannchew2534]

I'm glad that you find it useful. My time writing it had not been wasted :-)

[@AhmadBazzi]

It definitely was not. Gave me lots or room to improve and make the channel better and better. Thanks a lot, Kar !!

[@idryman]

This is beautiful. Thank you for creating this wonderful series.

[@hankpark4510]

First of all, huge respect for quality content! ---------------------------------------------------------------------------------------------- I have a question for y'Cy under y'y

[@AhmadBazzi]

Hello and welcome Hyuk Park, I'm really glad you found interest on the channel. ---------------------------------------------------------------------------------------------- For your question, notice that we did not restrict a PSD constraint (if we were to impose PSD then the case of \lambda_min < 0 does not make sense right ? ). Therefore, you are right to say "I guess that p* should be always the lambda_min given that "C" is PSD." This is equivalent to \lambda_min >= 0. As a correction, I did not mention " lamba_min can be less than 0 for the case of p* being 0." All I said was, if \lambda_min

[@mdforidul6232]

How

[@mdforidul6232]

How

[@YuxuanHarry]

I feel a little confused here. Using the proposition: EigenValue of the product of PSD matrix is all postive, we can conclude that C's eigenvalue is all postitive. So lambda_min is definitely larger than 0, then p* should always be 0 ???

[@AndrewFOguns]

...You did a great job in this course prof. I always look for your videos when I am trying to understand difficult topics in your area of expertise...You really take out time to explain concepts in details... Keep up the good work and may God bless you abundantly...

[@СергейИванов76]

Very interesting and informative video review !

[@Akshay-cy9tu]

just epic lecture

[@hbasu8779]

Thank you Professor Bazzi for the wonderful lecture. You have explained everything very nicely. I just have a minor question: for minimizing y^{T}Cy, why do we only focus on the eigendirections? Can we not find a minimum or maximum of the objective function y^{T}Cy along any other directions? It will be great if you can get a chance to respond to this. Thanks in advance.

[@nijilgeorge2905]

Thank you for the lecture, it helped me understand the concepts. I have a doubt at 23:50, why does alpha have to be positive, shouldn't Cauchy-Schwarz inequality hold any multiple of the vectors?

[@destimadya6217]

Thank you Dr. Bazzi. I have read that the QCQP can be solved using interior-point methods and these properties can be solved using Alternating Optimization (AO) algorithm. Would you explain more details about interior-point methods and Alternating Optimization (AO) algorithm? Thank you very much.

[@tahseensaad7860]

Dear Dr Ahmed Bazzi thanks for your valuable lecture. questions 1) how to formulate any problem (objective function) to QCQP? 2) if we formulate a problem in the form (X^T W X), what technique are used to check W is PSD? 3) In case W is hermitian, how would we check that W is and PSD? Regards

[@amritanand3165]

Thanks sir. Lectures are really very useful. But it would be much better if you will solve more numerical problem.

[@AhmadBazzi]

Hello Amrit, I'm glad you found it useful. You can check this playlist I've dedicated for real life numerical examples: kzbin.info/www/bejne/aWnYaWicfd2IY68

[@fahadshammary]

I really enjoy your videos, they are so useful for me especially the graphical explanation using matlab. I am learning a lot actually. are you uploading the onenote files ? I really appreciate your effort.

[@AhmadBazzi]

Thank you for your interest, Fahad. We're actually working on a website containing all the lectures in a well-written fashion.

[@hamzamalik1097]

@@AhmadBazzi Sir, How soon this website will be available for access? Waiting to get hands over your notes.

[@mayurkatwe4875]

Hello sir, the lecture was really interesting. I have a doubt. How to solve an optimization problem which have quadratic equality constraints. Kindly, help.

[@julescesar4779]

thank you for the helpfull effort sir. can anyone help me with a reference to a book to learn optimisation please

[@iamdrfly]

Hi, at 21:30 is not missing the abs value? |-c^T y|

[@sojonkumar5822]

Hello and welcome nice Video

[@shubhamsharma2202]

thank you for the lecture.. do you think it is possible to solve "Minimizing a quadratic function over an uncentered ellipsoid" ? thank you

[@AhmadBazzi]

You are welcome Shubham. Indeed, the same change of variable could be done as in the uncentered linear problem.

[@shubhamsharma2202]

@@AhmadBazzi thank you so mych sir

[@vasileioskosmidis1421]

too much detail getting boring

[@sarowersayem8606]

Why ? Ahmad is giving us a lot of useful information. If you find it boring, you can just go to another video without giving stupid nonsense comments

[@vasileioskosmidis1421]

@@sarowersayem8606 There is no need or asked for your ridiculous and stupid comments. Clearly you are not looking for improvement but you are happy with mediocracy.

[@mizan.1114]

Wow nice video qkksieoemd ajwoeodnbd aoqkejdb❤️❤️❤️❤️

[@youssefak8534]

Why ? Ahmad is giving us a lot of useful information. If you find it boring, you can just go to another video without giving stupid nonsense comments.