Operations Research 10B: Hessian Matrix, Convex & Concave Functions

Textbooks:

In this video, I'll talk about Hessian matrix, positive semidefinite matrix, negative semidefinite matrix, and convex and concave functions.

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[YongWang]

Hi Guys, please comment and let me know what you think about this Operations Research Open Course. Your feedback is really appreciated. If you enjoy the video, please subscribe and share. All my replies here are only related to the content in my own videos. I am afraid I won't be able to answer other questions. Thanks for your understanding.

[danmcgloven]

Great explanation. Btw, Prof. Ahmad Bazzi provides more insights on convex optimization !

Very clear explanation of the hessian matrix and some examples. Thank you Mr. Wang

[mykolalazarenko]

The amazingly simple explanation with great examples! Thank you very much!

[xlvubqb]

very simple, very good explanation, excellent examples . thank you Dr wang

[SheevStalin]

Thanks a lot for your video, I have an optimisation exam tomorrow morning this was very helpful!

[orangeraven]

Thank you for the clear explanation. One precision: on the screen around 2 m 49 s the third partial derivative appears as df/dx1 = 4x3 when in fact it's the derivative with respect to x3, so it should be df/dx3 = 4x3. Otherwise all good!

[gourabchanda]

Sir thank you so much! I am a beginner and this is the most lucid explanation that I have ever come across.

[lynguyen]

Thank you very much for your detailed explanation and concrete examples! I really appreciate it!

[vipinsagark]

superbly explained in an understandable way to all

[tstoof]

Really clear explanation with very helpful examples. Thank you very much!

[xiaoqingzhou]

Thank you so much for uploading, the given examples were sooo clear and easy to understand!! May I ask how to determine the function whether its quasiconvex or quasiconcave? Thanks!

[FrederikSchuetz]

Very helpful! Thanks a lot for putting the time and effort in for this video!

[ryanalfeldt]

On the 3x3 hessian example, you knew the final z equation was all greater than zero because the coefficients were all positive and the z’s were squared, what if my z’s aren’t all squared but all my coefficients are positive? Is it still positive semi definite?

[badisanaveen]

for finding the given function is convex or not. Is we have to do 2nd order derivatives for objective function is sufficient or we have to consider the constraints also or no need

[mrpuppydog]

Super well explained thanks so much for this explanation

[nitinkumarmittal]

Thank you for a clear explanation. I believe, there's a typo at 2:49 for partial derivative of f w.r.t to x_3

[_PraveenSingh_]

Is the hessian matrix always symmetric if the 2nd order P.DEs of function is continuous, like always? Is there a way to determine the convexity of a function if the Hessian matrix is not symmetric?

[underlecht]

Clear, short explanation. Perfect. Thank you.

[openpo]

thank you! I have a question: how to prove if the function is non convex (or even nonsmooth) function?