Operations Research 05C: Weak Duality & Strong Duality

[@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.

[@ajitrajendran63]

I presume when you mean excess variable, it is the same as slack variable?

[@YongWang]

Correction: At 7:00, I forgot to add the inverse "-1" for the matrix B [1 1 8; 0 1.5 4; 0 0.5 2] at the bottom left corner

[@zoedesvl4131]

Just a random guy who wants to tell you that I thought my operation research was done but with your help I got an A in the end and what's more important, I do understand these theories. I cannot thank you enough.

[@jdt9654]

Yong Wang, you are an outstanding teacher! I keep having one aha moment after another. Thank you so much!

[@shafiqshams3065]

The graphical explanation is outstanding. Thank you so much!

[@RanjeetKumar-nh7cn]

Thank you sir ..! It is very useful for me And you forgot to write inverse but you have written in your comments Thank you ...! Have a great day ...!

[@YongWang]

Thanks, for the comment, Ranjeet

[@nourhanelzoghby1605]

Are you solve last example by big-M method?? Because you add artificial variables a2 and a3??

[@fadygeorge8152]

there is an error in minute 7:00 in matrix multiplication the result is incorrect and i think you choose matrix B by mistake ! we should choose matrix from the primal optimal table but for the initial basic variable which we start by in the initial table

[@YongWang]

fady, there was an error at 7:00. see my other comment at the top of this comment area

[@TheJohannes4174]

What if the Primal is written in min and the dual therefore in max. Does this make the weak theorem different? Should it say c^Tx>b^Tv?

[@YongWang]

Johannes, you can always convert a max problem to a min problem by taking the opposite (-z) of the objective function. You can also convert a >= sign to a

[@vnaveenkumar982]

@@YongWang But as the OP said cant we take it in that format. which is (>).

[@ahududu9503]

Superb quality

[@YongWang]

Thanks, Faruk

[@yiwu403]

Very helpful. Thank you!

[@wigginskuang8244]

Hi Professor Wang, could you please explain what is the M in the strong duality part? (where you said that when the constraint is = in primal, ui=coeff of si in R0-M)

[@ahmadtalafha2742]

Well done! Thank you!

[@YongWang]

Thanks!

[@thanhphan2374]

I have a question: How are ai,j and aj,i different from one another? I watched the Dual and Primal video and understand how to derive dual from the primal but don't understand this expression in the standard form. Thank you in advance!

[@CSBSIRIKIVENKATASIVASURYASAI]

loved it !! Thanks

[@riccardovalsecchi8851]

how can you find the optimal solution for the dual with three variables? can i compute it with graphical solution?

[@YongWang]

Riccardo, you can find it using the graphical method or the simplex method. see videos 04A-04H of this open course kzbin.info/www/bejne/nGSqq2eJfLaJb68

[@cansuvural2126]

Harika!! Thank you!

[@YongWang]

thanks, cansu

[@CarlosMatamala]

One question: Are the weak and the strong duality theorems valid only for linear problems?

[@YongWang]

Carlos, for nonlinear problems, you may refer to en.wikipedia.org/wiki/Duality_(optimization)#Nonlinear_case

[@VinVin21969]

@@YongWang how to differentiate weak and strong ?? if in weak duality primal opt solution can be equal to dual opt solution??

[@soumithnalli5169]

Thank you sir

[@YongWang]

you are welcome, soumith

[@karishmakumawat4175]

Thank you sir!!

[@Ivon_vlog]

What’s the meaning of e2 in the title of the column?

[@dungeon_daddy9131]

Wang gang !

[@Nur98162]

i love you :)))

[@YongWang]

Thanks, Nur