Lecture 14 | Lagrange Dual Function | Convex Optimization by Dr. Ahmad Bazzi

[@AhmadBazzi]

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[@jeanishimwe2120]

Thanks Dr. You brought it on the right time. It helps understanding duality.

[@AhmadBazzi]

you are most welcome :)

[@aleocho774]

@@AhmadBazzi thanks a lot sir

[@hbasu8779]

In two-way partitioning example problem at @24:25, when W+V is not PSD, then how do you get the cost -infinity? I am asking this because x can only take values +1 or -1. If you say that when a constrained optimization becomes an unconstrained optimization problem, thanks to the Lagrange function, x does not come from domain D of feasible space of the original problem (which in this case takes on +1 or -1 values) but comes from euclidean space R^n, then isn't the domain of Lagrange function @3.38 wrong? if dom L(x,, : , :) = D * R^m* R^p then in the two-way partitioning example the cost cannot be inifnity,

[@SaikSaketh]

Thanks. Right on time matching lectures at University. Thanks

[@AhmadBazzi]

You are most welcome !!

[@iamdrfly]

at 31:52 should it be sup{y^T*x - ||x||} instead ... + ||x||?

[@positivobro8544]

At 20:15 , isn't the condition actually that c-lambda-A^T v >=0 ? Because if all values of the gradient of the lagrangian are positive and your feasible x's are constrained to be positive than you can only increase the function and the minimal x is x=0 giving the same dual function value as the =0 case. Right?

[@mohammadsarkhosh935]

in 25:11 why inf xT (w+v)x isn't gradian x which is equal to 2*xT(w+x) . Where did Lamda come from when you wrote Lamda min?

[@localcarbuyer8704]

well described!!!

[@AhmadBazzi]

Glad you think so!

[@jhonatancollazosramirez8513]

these exercise min 15:35 How would it be programmed in MatLab? thank you

[@hbasu8779]

why is g(\lambda,\mu) concave at @6.46?

[@AK-yf4dp]

Thank you Dr,Ahmad for an amazing course!! I have a question, in the Matlab example the value of x obtain by fminunc solver was 0.1574 which clearly is not optimal value (x star) , what is the reason of that?

[@danmcgloven8169]

From my experience, it's better to leave a timestamp on the exact minute so you get faster responses from Ahmad. Notice how he responds on timestamped questions.

[@santhuathidi5987]

hello sir.. in 34:49 how f0*(y)= sum(exp(yi-1)) from f0(x) pls explain

[@aleocho774]

The conjugate function of sum(xi log xi) is sum(exp(yi-1))

[@saumyachaturvedi9065]

Thanks, sir. Sir, how to proceed if we have more than one Lagrange multiplier, especially for Matlab. How to find the optimal value of Lagrange multipliers in that case?

[@chrisliou2323]

Hi, at 8:39 and 8:45, did you mean "upper bounded by" rather than "lower bounded by" ?

[@AhmadBazzi]

yes you are right, Chris. Thanks for pointing this out !!

[@ArmanAli-ww7ml]

what happen if we open infimum term with lagrangian function inside?

[@thomasjefferson6225]

Anyone know why he converted x >= 0 to -x

[@sepidehghasemi8631]

thank you for amazing course, now I understand better😊 I need help about one example in Optimization course. Can you help me please?

[@momofrozen4431]

Can you please explain the derivative of vT(Ax-b)=ATv?

[@AhmadBazzi]

Hey Momo, well the derivative of your expression is the same as the derivative of vTAx since vTb is independent of x. So now let’s deal with vTAx. Write down the expression as a summation then derive with respect to the kth entry of x, x_k. Finally stack all the derivatives one on top of the other.

[@sepidehghasemi8631]

If I join in your group, Can I send you my question about Optimization?

[@imtryinghere1]

is it me or does he go through the matlab code really fast? I guess because I am only a python scrub it is a bit fast for me to follow the code...

[@ehsaneshaghi3613]

There are too many distracting advertisements !

[@danmcgloven8169]

Why you hating man ? I think it's pretty okay if there's ads when ahmad dedicates time to get rewarded